How do you find the volume of the solid generated when the regions bounded by the graphs of the given equations #y = root3x#, x = 0, x = 8 and the x-axis are rotated about the x-axis?

Question

Christopher Agresta · Accepted Answer

#96/5pi# Rotation about #x# axis, hence #piinty^2dx# #y^2 = (x^(1/3))^2 = x^(2/3)# #=piint_0^8x^(2/3)dx# #= [3/5x^(5/3)]_0^8 # #= 3/5pi((8/5)^(5/3)-0^(5/3))# #= 96/5pi#

Cameron Alexander · Answer

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To find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

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The volume $V$ of the solid is given by the formula:

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The volume $V$ of the solid is given by the formula:

\[V = 2\pi \int_{To find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

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\[V = 2\pi \int_{aTo find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

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The volume $V$ of the solid is given by the formula:

\[V = 2\pi \int_{a}To find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$To find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

\[V = 2\pi \int_{a}^{To find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ canTo find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

\[V = 2\pi \int_{a}^{b}To find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

\[ V =To find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

\[V = 2\pi \int_{a}^{b} xTo find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

\[ V = \To find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

\[V = 2\pi \int_{a}^{b} x \To find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

\[ V = \intTo find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

\[V = 2\pi \int_{a}^{b} x \cdotTo find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

\[ V = \int_{To find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

\[V = 2\pi \int_{a}^{b} x \cdot fTo find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

\[ V = \int_{aTo find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

\[V = 2\pi \int_{a}^{b} x \cdot f(xTo find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

\[ V = \int_{a}To find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

\[V = 2\pi \int_{a}^{b} x \cdot f(x)To find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

\[ V = \int_{a}^{To find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

\[V = 2\pi \int_{a}^{b} x \cdot f(x) \To find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

\[ V = \int_{a}^{bTo find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

\[V = 2\pi \int_{a}^{b} x \cdot f(x) \,To find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

\[ V = \int_{a}^{b}To find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

\[V = 2\pi \int_{a}^{b} x \cdot f(x) \, dxTo find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

$$ V = \int_{a}^{b} To find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

\[V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx\To find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

\[ V = \int_{a}^{b} 2To find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

\[V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

To find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

$$ V = \int_{a}^{b} 2\To find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

\[V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

whereTo find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

$$ V = \int_{a}^{b} 2\piTo find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

\[V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $aTo find the volume of the solid generated when the region bounded by the graphs of \(y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

$$ V = \int_{a}^{b} 2\pi xTo find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

\[V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$To find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

$$ V = \int_{a}^{b} 2\pi x fTo find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

\[V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ andTo find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

$$ V = \int_{a}^{b} 2\pi x f(xTo find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

\[V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $To find the volume of the solid generated when the region bounded by the graphs of \(y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

$$ V = \int_{a}^{b} 2\pi x f(x)To find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

\[V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $bTo find the volume of the solid generated when the region bounded by the graphs of \(y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

$$ V = \int_{a}^{b} 2\pi x f(x) \To find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

\[V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$To find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

$$ V = \int_{a}^{b} 2\pi x f(x) \,To find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

\[V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ areTo find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

$$ V = \int_{a}^{b} 2\pi x f(x) \, dxTo find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

\[V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the xTo find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

$$ V = \int_{a}^{b} 2\pi x f(x) \, dx \To find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

\[V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-valuesTo find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

$$ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

To find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

$$V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where theTo find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

$$ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

whereTo find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

$$V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curvesTo find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

$$ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $To find the volume of the solid generated when the regions bounded by the graphs of \(y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

$$V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersectTo find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

$$ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $aTo find the volume of the solid generated when the regions bounded by the graphs of \(y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

$$V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect,To find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

$$ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$To find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

$$V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, andTo find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

$$ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$ andTo find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

$$V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, and $To find the volume of the solid generated when the region bounded by the graphs of \(y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

$$ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$ and $To find the volume of the solid generated when the regions bounded by the graphs of \(y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

$$V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, and $fTo find the volume of the solid generated when the region bounded by the graphs of \(y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

$$ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$ and $bTo find the volume of the solid generated when the regions bounded by the graphs of \(y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

$$V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, and $f(xTo find the volume of the solid generated when the region bounded by the graphs of \(y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

$$ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$ and $b$To find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

$$V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, and $f(x)\To find the volume of the solid generated when the region bounded by the graphs of \(y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

$$ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$ and $b$ areTo find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

$$V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, and $f(x)$To find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

$$ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$ and $b$ are theTo find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

$$V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, and $f(x)$ is theTo find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

$$ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$ and $b$ are the limits ofTo find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

$$V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, and $f(x)$ is the height of theTo find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

$$ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$ and $b$ are the limits of integrationTo find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

$$V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, and $f(x)$ is the height of the shellTo find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

$$ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$ and $b$ are the limits of integration,To find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

$$V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, and $f(x)$ is the height of the shell atTo find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

$$ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$ and $b$ are the limits of integration, andTo find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

$$V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, and $f(x)$ is the height of the shell at eachTo find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

$$ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$ and $b$ are the limits of integration, and $To find the volume of the solid generated when the regions bounded by the graphs of \(y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

$$V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, and $f(x)$ is the height of the shell at each xTo find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

$$ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$ and $b$ are the limits of integration, and $fTo find the volume of the solid generated when the regions bounded by the graphs of \(y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

$$V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, and $f(x)$ is the height of the shell at each x-value.

To find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

$$ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$ and $b$ are the limits of integration, and $f(xTo find the volume of the solid generated when the regions bounded by the graphs of \(y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

$$V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, and $f(x)$ is the height of the shell at each x-value.

InTo find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

$$ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$ and $b$ are the limits of integration, and $f(x)\To find the volume of the solid generated when the regions bounded by the graphs of \(y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

$$V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, and $f(x)$ is the height of the shell at each x-value.

In this caseTo find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

$$ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$ and $b$ are the limits of integration, and $f(x)$To find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

$$V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, and $f(x)$ is the height of the shell at each x-value.

In this case,To find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

$$ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$ and $b$ are the limits of integration, and $f(x)$ representsTo find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

$$V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, and $f(x)$ is the height of the shell at each x-value.

In this case, theTo find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

$$ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$ and $b$ are the limits of integration, and $f(x)$ represents theTo find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

$$V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, and $f(x)$ is the height of the shell at each x-value.

In this case, the curves intersectTo find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

$$ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$ and $b$ are the limits of integration, and $f(x)$ represents the functionTo find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

$$V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, and $f(x)$ is the height of the shell at each x-value.

In this case, the curves intersect atTo find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

$$ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$ and $b$ are the limits of integration, and $f(x)$ represents the function describingTo find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

$$V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, and $f(x)$ is the height of the shell at each x-value.

In this case, the curves intersect at $To find the volume of the solid generated when the region bounded by the graphs of \(y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

$$ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$ and $b$ are the limits of integration, and $f(x)$ represents the function describing theTo find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

$$V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, and $f(x)$ is the height of the shell at each x-value.

In this case, the curves intersect at $xTo find the volume of the solid generated when the region bounded by the graphs of \(y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

$$ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$ and $b$ are the limits of integration, and $f(x)$ represents the function describing the heightTo find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

$$V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, and $f(x)$ is the height of the shell at each x-value.

In this case, the curves intersect at $x = 0To find the volume of the solid generated when the region bounded by the graphs of \(y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

$$ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$ and $b$ are the limits of integration, and $f(x)$ represents the function describing the height of the shell at each point.

ForTo find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

$$V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, and $f(x)$ is the height of the shell at each x-value.

In this case, the curves intersect at $x = 0$ andTo find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

$$ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$ and $b$ are the limits of integration, and $f(x)$ represents the function describing the height of the shell at each point.

For this problemTo find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

$$V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, and $f(x)$ is the height of the shell at each x-value.

In this case, the curves intersect at $x = 0$ and $To find the volume of the solid generated when the region bounded by the graphs of \(y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

$$ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$ and $b$ are the limits of integration, and $f(x)$ represents the function describing the height of the shell at each point.

For this problem,To find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

$$V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, and $f(x)$ is the height of the shell at each x-value.

In this case, the curves intersect at $x = 0$ and $xTo find the volume of the solid generated when the region bounded by the graphs of \(y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

$$ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$ and $b$ are the limits of integration, and $f(x)$ represents the function describing the height of the shell at each point.

For this problem, $To find the volume of the solid generated when the regions bounded by the graphs of \(y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

$$V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, and $f(x)$ is the height of the shell at each x-value.

In this case, the curves intersect at $x = 0$ and $x = To find the volume of the solid generated when the region bounded by the graphs of \(y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

$$ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$ and $b$ are the limits of integration, and $f(x)$ represents the function describing the height of the shell at each point.

For this problem, $aTo find the volume of the solid generated when the regions bounded by the graphs of \(y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

$$V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, and $f(x)$ is the height of the shell at each x-value.

In this case, the curves intersect at $x = 0$ and $x = 8To find the volume of the solid generated when the region bounded by the graphs of \(y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

$$ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$ and $b$ are the limits of integration, and $f(x)$ represents the function describing the height of the shell at each point.

For this problem, $a =To find the volume of the solid generated when the regions bounded by the graphs of \(y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

$$V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, and $f(x)$ is the height of the shell at each x-value.

In this case, the curves intersect at $x = 0$ and $x = 8\To find the volume of the solid generated when the region bounded by the graphs of \(y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

$$ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$ and $b$ are the limits of integration, and $f(x)$ represents the function describing the height of the shell at each point.

For this problem, $a = To find the volume of the solid generated when the regions bounded by the graphs of \(y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

$$V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, and $f(x)$ is the height of the shell at each x-value.

In this case, the curves intersect at $x = 0$ and $x = 8$, soTo find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

$$ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$ and $b$ are the limits of integration, and $f(x)$ represents the function describing the height of the shell at each point.

For this problem, $a = 0To find the volume of the solid generated when the regions bounded by the graphs of \(y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

$$V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, and $f(x)$ is the height of the shell at each x-value.

In this case, the curves intersect at $x = 0$ and $x = 8$, so theTo find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

$$ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$ and $b$ are the limits of integration, and $f(x)$ represents the function describing the height of the shell at each point.

For this problem, $a = 0$To find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

$$V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, and $f(x)$ is the height of the shell at each x-value.

In this case, the curves intersect at $x = 0$ and $x = 8$, so the integralTo find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

$$ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$ and $b$ are the limits of integration, and $f(x)$ represents the function describing the height of the shell at each point.

For this problem, $a = 0$ andTo find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

$$V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, and $f(x)$ is the height of the shell at each x-value.

In this case, the curves intersect at $x = 0$ and $x = 8$, so the integral becomes:

To find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

$$ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$ and $b$ are the limits of integration, and $f(x)$ represents the function describing the height of the shell at each point.

For this problem, $a = 0$ and $To find the volume of the solid generated when the regions bounded by the graphs of \(y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

$$V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, and $f(x)$ is the height of the shell at each x-value.

In this case, the curves intersect at $x = 0$ and $x = 8$, so the integral becomes:

$$To find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

\[ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$ and $b$ are the limits of integration, and $f(x)$ represents the function describing the height of the shell at each point.

For this problem, $a = 0$ and $bTo find the volume of the solid generated when the regions bounded by the graphs of \(y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

$$V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, and $f(x)$ is the height of the shell at each x-value.

In this case, the curves intersect at $x = 0$ and $x = 8$, so the integral becomes:

$$VTo find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

\[ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$ and $b$ are the limits of integration, and $f(x)$ represents the function describing the height of the shell at each point.

For this problem, $a = 0$ and $b =To find the volume of the solid generated when the regions bounded by the graphs of \(y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

$$V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, and $f(x)$ is the height of the shell at each x-value.

In this case, the curves intersect at $x = 0$ and $x = 8$, so the integral becomes:

$$V =To find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

\[ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$ and $b$ are the limits of integration, and $f(x)$ represents the function describing the height of the shell at each point.

For this problem, $a = 0$ and $b = To find the volume of the solid generated when the regions bounded by the graphs of \(y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

$$V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, and $f(x)$ is the height of the shell at each x-value.

In this case, the curves intersect at $x = 0$ and $x = 8$, so the integral becomes:

$$V = 2To find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

\[ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$ and $b$ are the limits of integration, and $f(x)$ represents the function describing the height of the shell at each point.

For this problem, $a = 0$ and $b = 8\To find the volume of the solid generated when the regions bounded by the graphs of \(y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

$$V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, and $f(x)$ is the height of the shell at each x-value.

In this case, the curves intersect at $x = 0$ and $x = 8$, so the integral becomes:

$$V = 2\piTo find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

\[ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$ and $b$ are the limits of integration, and $f(x)$ represents the function describing the height of the shell at each point.

For this problem, $a = 0$ and $b = 8$, andTo find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

$$V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, and $f(x)$ is the height of the shell at each x-value.

In this case, the curves intersect at $x = 0$ and $x = 8$, so the integral becomes:

$$V = 2\pi \To find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

\[ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$ and $b$ are the limits of integration, and $f(x)$ represents the function describing the height of the shell at each point.

For this problem, $a = 0$ and $b = 8$, and $fTo find the volume of the solid generated when the regions bounded by the graphs of \(y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

$$V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, and $f(x)$ is the height of the shell at each x-value.

In this case, the curves intersect at $x = 0$ and $x = 8$, so the integral becomes:

$$V = 2\pi \int_{To find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

\[ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$ and $b$ are the limits of integration, and $f(x)$ represents the function describing the height of the shell at each point.

For this problem, $a = 0$ and $b = 8$, and $f(xTo find the volume of the solid generated when the regions bounded by the graphs of \(y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

$$V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, and $f(x)$ is the height of the shell at each x-value.

In this case, the curves intersect at $x = 0$ and $x = 8$, so the integral becomes:

$$V = 2\pi \int_{0To find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

\[ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$ and $b$ are the limits of integration, and $f(x)$ represents the function describing the height of the shell at each point.

For this problem, $a = 0$ and $b = 8$, and $f(x) =To find the volume of the solid generated when the regions bounded by the graphs of \(y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

$$V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, and $f(x)$ is the height of the shell at each x-value.

In this case, the curves intersect at $x = 0$ and $x = 8$, so the integral becomes:

$$V = 2\pi \int_{0}^{To find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

\[ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$ and $b$ are the limits of integration, and $f(x)$ represents the function describing the height of the shell at each point.

For this problem, $a = 0$ and $b = 8$, and $f(x) = \sqrtTo find the volume of the solid generated when the regions bounded by the graphs of \(y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

$$V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, and $f(x)$ is the height of the shell at each x-value.

In this case, the curves intersect at $x = 0$ and $x = 8$, so the integral becomes:

$$V = 2\pi \int_{0}^{8}To find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

\[ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$ and $b$ are the limits of integration, and $f(x)$ represents the function describing the height of the shell at each point.

For this problem, $a = 0$ and $b = 8$, and $f(x) = \sqrt{To find the volume of the solid generated when the regions bounded by the graphs of \(y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

$$V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, and $f(x)$ is the height of the shell at each x-value.

In this case, the curves intersect at $x = 0$ and $x = 8$, so the integral becomes:

$$V = 2\pi \int_{0}^{8} xTo find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

\[ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$ and $b$ are the limits of integration, and $f(x)$ represents the function describing the height of the shell at each point.

For this problem, $a = 0$ and $b = 8$, and $f(x) = \sqrt{3To find the volume of the solid generated when the regions bounded by the graphs of \(y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

$$V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, and $f(x)$ is the height of the shell at each x-value.

In this case, the curves intersect at $x = 0$ and $x = 8$, so the integral becomes:

$$V = 2\pi \int_{0}^{8} x \To find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

\[ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$ and $b$ are the limits of integration, and $f(x)$ represents the function describing the height of the shell at each point.

For this problem, $a = 0$ and $b = 8$, and $f(x) = \sqrt{3xTo find the volume of the solid generated when the regions bounded by the graphs of \(y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

$$V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, and $f(x)$ is the height of the shell at each x-value.

In this case, the curves intersect at $x = 0$ and $x = 8$, so the integral becomes:

$$V = 2\pi \int_{0}^{8} x \cdotTo find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

\[ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$ and $b$ are the limits of integration, and $f(x)$ represents the function describing the height of the shell at each point.

For this problem, $a = 0$ and $b = 8$, and $f(x) = \sqrt{3x}\To find the volume of the solid generated when the regions bounded by the graphs of \(y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

$$V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, and $f(x)$ is the height of the shell at each x-value.

In this case, the curves intersect at $x = 0$ and $x = 8$, so the integral becomes:

$$V = 2\pi \int_{0}^{8} x \cdot \To find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

\[ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$ and $b$ are the limits of integration, and $f(x)$ represents the function describing the height of the shell at each point.

For this problem, $a = 0$ and $b = 8$, and $f(x) = \sqrt{3x}$.To find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

$$V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, and $f(x)$ is the height of the shell at each x-value.

In this case, the curves intersect at $x = 0$ and $x = 8$, so the integral becomes:

$$V = 2\pi \int_{0}^{8} x \cdot \sqrtTo find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

\[ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$ and $b$ are the limits of integration, and $f(x)$ represents the function describing the height of the shell at each point.

For this problem, $a = 0$ and $b = 8$, and $f(x) = \sqrt{3x}$. SubTo find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

$$V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, and $f(x)$ is the height of the shell at each x-value.

In this case, the curves intersect at $x = 0$ and $x = 8$, so the integral becomes:

$$V = 2\pi \int_{0}^{8} x \cdot \sqrt{To find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

\[ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$ and $b$ are the limits of integration, and $f(x)$ represents the function describing the height of the shell at each point.

For this problem, $a = 0$ and $b = 8$, and $f(x) = \sqrt{3x}$. SubstitTo find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

$$V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, and $f(x)$ is the height of the shell at each x-value.

In this case, the curves intersect at $x = 0$ and $x = 8$, so the integral becomes:

$$V = 2\pi \int_{0}^{8} x \cdot \sqrt{3To find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

\[ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$ and $b$ are the limits of integration, and $f(x)$ represents the function describing the height of the shell at each point.

For this problem, $a = 0$ and $b = 8$, and $f(x) = \sqrt{3x}$. SubstitutingTo find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

$$V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, and $f(x)$ is the height of the shell at each x-value.

In this case, the curves intersect at $x = 0$ and $x = 8$, so the integral becomes:

$$V = 2\pi \int_{0}^{8} x \cdot \sqrt{3xTo find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

\[ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$ and $b$ are the limits of integration, and $f(x)$ represents the function describing the height of the shell at each point.

For this problem, $a = 0$ and $b = 8$, and $f(x) = \sqrt{3x}$. Substituting theseTo find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

$$V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, and $f(x)$ is the height of the shell at each x-value.

In this case, the curves intersect at $x = 0$ and $x = 8$, so the integral becomes:

$$V = 2\pi \int_{0}^{8} x \cdot \sqrt{3x} \To find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

\[ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$ and $b$ are the limits of integration, and $f(x)$ represents the function describing the height of the shell at each point.

For this problem, $a = 0$ and $b = 8$, and $f(x) = \sqrt{3x}$. Substituting these valuesTo find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

$$V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, and $f(x)$ is the height of the shell at each x-value.

In this case, the curves intersect at $x = 0$ and $x = 8$, so the integral becomes:

$$V = 2\pi \int_{0}^{8} x \cdot \sqrt{3x} \,To find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

\[ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$ and $b$ are the limits of integration, and $f(x)$ represents the function describing the height of the shell at each point.

For this problem, $a = 0$ and $b = 8$, and $f(x) = \sqrt{3x}$. Substituting these values intoTo find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

$$V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, and $f(x)$ is the height of the shell at each x-value.

In this case, the curves intersect at $x = 0$ and $x = 8$, so the integral becomes:

$$V = 2\pi \int_{0}^{8} x \cdot \sqrt{3x} \, dxTo find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

\[ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$ and $b$ are the limits of integration, and $f(x)$ represents the function describing the height of the shell at each point.

For this problem, $a = 0$ and $b = 8$, and $f(x) = \sqrt{3x}$. Substituting these values into theTo find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

$$V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, and $f(x)$ is the height of the shell at each x-value.

In this case, the curves intersect at $x = 0$ and $x = 8$, so the integral becomes:

$$V = 2\pi \int_{0}^{8} x \cdot \sqrt{3x} \, dx\To find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

\[ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$ and $b$ are the limits of integration, and $f(x)$ represents the function describing the height of the shell at each point.

For this problem, $a = 0$ and $b = 8$, and $f(x) = \sqrt{3x}$. Substituting these values into the formulaTo find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

$$V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, and $f(x)$ is the height of the shell at each x-value.

In this case, the curves intersect at $x = 0$ and $x = 8$, so the integral becomes:

$$V = 2\pi \int_{0}^{8} x \cdot \sqrt{3x} \, dx$$

To find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

$$ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$ and $b$ are the limits of integration, and $f(x)$ represents the function describing the height of the shell at each point.

For this problem, $a = 0$ and $b = 8$, and $f(x) = \sqrt{3x}$. Substituting these values into the formula,To find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

$$V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, and $f(x)$ is the height of the shell at each x-value.

In this case, the curves intersect at $x = 0$ and $x = 8$, so the integral becomes:

$$V = 2\pi \int_{0}^{8} x \cdot \sqrt{3x} \, dx$$

SimplTo find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

$$ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$ and $b$ are the limits of integration, and $f(x)$ represents the function describing the height of the shell at each point.

For this problem, $a = 0$ and $b = 8$, and $f(x) = \sqrt{3x}$. Substituting these values into the formula, we haveTo find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

$$V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, and $f(x)$ is the height of the shell at each x-value.

In this case, the curves intersect at $x = 0$ and $x = 8$, so the integral becomes:

$$V = 2\pi \int_{0}^{8} x \cdot \sqrt{3x} \, dx$$

SimplifyingTo find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

$$ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$ and $b$ are the limits of integration, and $f(x)$ represents the function describing the height of the shell at each point.

For this problem, $a = 0$ and $b = 8$, and $f(x) = \sqrt{3x}$. Substituting these values into the formula, we have:

To find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

$$V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, and $f(x)$ is the height of the shell at each x-value.

In this case, the curves intersect at $x = 0$ and $x = 8$, so the integral becomes:

$$V = 2\pi \int_{0}^{8} x \cdot \sqrt{3x} \, dx$$

Simplifying theTo find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

$$ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$ and $b$ are the limits of integration, and $f(x)$ represents the function describing the height of the shell at each point.

For this problem, $a = 0$ and $b = 8$, and $f(x) = \sqrt{3x}$. Substituting these values into the formula, we have:

$$To find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

\[V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, and $f(x)$ is the height of the shell at each x-value.

In this case, the curves intersect at $x = 0$ and $x = 8$, so the integral becomes:

$$V = 2\pi \int_{0}^{8} x \cdot \sqrt{3x} \, dx$$

Simplifying the integrTo find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

$$ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$ and $b$ are the limits of integration, and $f(x)$ represents the function describing the height of the shell at each point.

For this problem, $a = 0$ and $b = 8$, and $f(x) = \sqrt{3x}$. Substituting these values into the formula, we have:

$$ VTo find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

\[V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, and $f(x)$ is the height of the shell at each x-value.

In this case, the curves intersect at $x = 0$ and $x = 8$, so the integral becomes:

$$V = 2\pi \int_{0}^{8} x \cdot \sqrt{3x} \, dx$$

Simplifying the integrandTo find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

$$ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$ and $b$ are the limits of integration, and $f(x)$ represents the function describing the height of the shell at each point.

For this problem, $a = 0$ and $b = 8$, and $f(x) = \sqrt{3x}$. Substituting these values into the formula, we have:

$$ V =To find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

\[V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, and $f(x)$ is the height of the shell at each x-value.

In this case, the curves intersect at $x = 0$ and $x = 8$, so the integral becomes:

$$V = 2\pi \int_{0}^{8} x \cdot \sqrt{3x} \, dx$$

Simplifying the integrand:

To find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

$$ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$ and $b$ are the limits of integration, and $f(x)$ represents the function describing the height of the shell at each point.

For this problem, $a = 0$ and $b = 8$, and $f(x) = \sqrt{3x}$. Substituting these values into the formula, we have:

$$ V = \To find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

\[V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, and $f(x)$ is the height of the shell at each x-value.

In this case, the curves intersect at $x = 0$ and $x = 8$, so the integral becomes:

$$V = 2\pi \int_{0}^{8} x \cdot \sqrt{3x} \, dx$$

Simplifying the integrand:

$$To find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

\[ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$ and $b$ are the limits of integration, and $f(x)$ represents the function describing the height of the shell at each point.

For this problem, $a = 0$ and $b = 8$, and $f(x) = \sqrt{3x}$. Substituting these values into the formula, we have:

$$ V = \intTo find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

\[V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, and $f(x)$ is the height of the shell at each x-value.

In this case, the curves intersect at $x = 0$ and $x = 8$, so the integral becomes:

$$V = 2\pi \int_{0}^{8} x \cdot \sqrt{3x} \, dx$$

Simplifying the integrand:

$$VTo find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

\[ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$ and $b$ are the limits of integration, and $f(x)$ represents the function describing the height of the shell at each point.

For this problem, $a = 0$ and $b = 8$, and $f(x) = \sqrt{3x}$. Substituting these values into the formula, we have:

$$ V = \int_{To find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

\[V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, and $f(x)$ is the height of the shell at each x-value.

In this case, the curves intersect at $x = 0$ and $x = 8$, so the integral becomes:

$$V = 2\pi \int_{0}^{8} x \cdot \sqrt{3x} \, dx$$

Simplifying the integrand:

$$V =To find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

\[ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$ and $b$ are the limits of integration, and $f(x)$ represents the function describing the height of the shell at each point.

For this problem, $a = 0$ and $b = 8$, and $f(x) = \sqrt{3x}$. Substituting these values into the formula, we have:

$$ V = \int_{0To find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

\[V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, and $f(x)$ is the height of the shell at each x-value.

In this case, the curves intersect at $x = 0$ and $x = 8$, so the integral becomes:

$$V = 2\pi \int_{0}^{8} x \cdot \sqrt{3x} \, dx$$

Simplifying the integrand:

$$V = 2To find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

\[ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$ and $b$ are the limits of integration, and $f(x)$ represents the function describing the height of the shell at each point.

For this problem, $a = 0$ and $b = 8$, and $f(x) = \sqrt{3x}$. Substituting these values into the formula, we have:

$$ V = \int_{0}To find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

\[V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, and $f(x)$ is the height of the shell at each x-value.

In this case, the curves intersect at $x = 0$ and $x = 8$, so the integral becomes:

$$V = 2\pi \int_{0}^{8} x \cdot \sqrt{3x} \, dx$$

Simplifying the integrand:

$$V = 2\To find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

\[ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$ and $b$ are the limits of integration, and $f(x)$ represents the function describing the height of the shell at each point.

For this problem, $a = 0$ and $b = 8$, and $f(x) = \sqrt{3x}$. Substituting these values into the formula, we have:

$$ V = \int_{0}^{To find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

\[V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, and $f(x)$ is the height of the shell at each x-value.

In this case, the curves intersect at $x = 0$ and $x = 8$, so the integral becomes:

$$V = 2\pi \int_{0}^{8} x \cdot \sqrt{3x} \, dx$$

Simplifying the integrand:

$$V = 2\pi \To find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

\[ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$ and $b$ are the limits of integration, and $f(x)$ represents the function describing the height of the shell at each point.

For this problem, $a = 0$ and $b = 8$, and $f(x) = \sqrt{3x}$. Substituting these values into the formula, we have:

$$ V = \int_{0}^{8To find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

\[V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, and $f(x)$ is the height of the shell at each x-value.

In this case, the curves intersect at $x = 0$ and $x = 8$, so the integral becomes:

$$V = 2\pi \int_{0}^{8} x \cdot \sqrt{3x} \, dx$$

Simplifying the integrand:

$$V = 2\pi \intTo find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

\[ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$ and $b$ are the limits of integration, and $f(x)$ represents the function describing the height of the shell at each point.

For this problem, $a = 0$ and $b = 8$, and $f(x) = \sqrt{3x}$. Substituting these values into the formula, we have:

$$ V = \int_{0}^{8}To find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

\[V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, and $f(x)$ is the height of the shell at each x-value.

In this case, the curves intersect at $x = 0$ and $x = 8$, so the integral becomes:

$$V = 2\pi \int_{0}^{8} x \cdot \sqrt{3x} \, dx$$

Simplifying the integrand:

$$V = 2\pi \int_{To find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

\[ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$ and $b$ are the limits of integration, and $f(x)$ represents the function describing the height of the shell at each point.

For this problem, $a = 0$ and $b = 8$, and $f(x) = \sqrt{3x}$. Substituting these values into the formula, we have:

$$ V = \int_{0}^{8} To find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

\[V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, and $f(x)$ is the height of the shell at each x-value.

In this case, the curves intersect at $x = 0$ and $x = 8$, so the integral becomes:

$$V = 2\pi \int_{0}^{8} x \cdot \sqrt{3x} \, dx$$

Simplifying the integrand:

$$V = 2\pi \int_{0}To find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

\[ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$ and $b$ are the limits of integration, and $f(x)$ represents the function describing the height of the shell at each point.

For this problem, $a = 0$ and $b = 8$, and $f(x) = \sqrt{3x}$. Substituting these values into the formula, we have:

$$ V = \int_{0}^{8} 2To find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

\[V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, and $f(x)$ is the height of the shell at each x-value.

In this case, the curves intersect at $x = 0$ and $x = 8$, so the integral becomes:

$$V = 2\pi \int_{0}^{8} x \cdot \sqrt{3x} \, dx$$

Simplifying the integrand:

$$V = 2\pi \int_{0}^{8To find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

\[ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$ and $b$ are the limits of integration, and $f(x)$ represents the function describing the height of the shell at each point.

For this problem, $a = 0$ and $b = 8$, and $f(x) = \sqrt{3x}$. Substituting these values into the formula, we have:

$$ V = \int_{0}^{8} 2\To find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

\[V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, and $f(x)$ is the height of the shell at each x-value.

In this case, the curves intersect at $x = 0$ and $x = 8$, so the integral becomes:

$$V = 2\pi \int_{0}^{8} x \cdot \sqrt{3x} \, dx$$

Simplifying the integrand:

$$V = 2\pi \int_{0}^{8}To find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

\[ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$ and $b$ are the limits of integration, and $f(x)$ represents the function describing the height of the shell at each point.

For this problem, $a = 0$ and $b = 8$, and $f(x) = \sqrt{3x}$. Substituting these values into the formula, we have:

$$ V = \int_{0}^{8} 2\piTo find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

\[V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, and $f(x)$ is the height of the shell at each x-value.

In this case, the curves intersect at $x = 0$ and $x = 8$, so the integral becomes:

$$V = 2\pi \int_{0}^{8} x \cdot \sqrt{3x} \, dx$$

Simplifying the integrand:

$$V = 2\pi \int_{0}^{8} xTo find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

\[ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$ and $b$ are the limits of integration, and $f(x)$ represents the function describing the height of the shell at each point.

For this problem, $a = 0$ and $b = 8$, and $f(x) = \sqrt{3x}$. Substituting these values into the formula, we have:

$$ V = \int_{0}^{8} 2\pi xTo find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

\[V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, and $f(x)$ is the height of the shell at each x-value.

In this case, the curves intersect at $x = 0$ and $x = 8$, so the integral becomes:

$$V = 2\pi \int_{0}^{8} x \cdot \sqrt{3x} \, dx$$

Simplifying the integrand:

$$V = 2\pi \int_{0}^{8} x^To find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

\[ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$ and $b$ are the limits of integration, and $f(x)$ represents the function describing the height of the shell at each point.

For this problem, $a = 0$ and $b = 8$, and $f(x) = \sqrt{3x}$. Substituting these values into the formula, we have:

$$ V = \int_{0}^{8} 2\pi x \To find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

\[V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, and $f(x)$ is the height of the shell at each x-value.

In this case, the curves intersect at $x = 0$ and $x = 8$, so the integral becomes:

$$V = 2\pi \int_{0}^{8} x \cdot \sqrt{3x} \, dx$$

Simplifying the integrand:

$$V = 2\pi \int_{0}^{8} x^{\To find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

\[ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$ and $b$ are the limits of integration, and $f(x)$ represents the function describing the height of the shell at each point.

For this problem, $a = 0$ and $b = 8$, and $f(x) = \sqrt{3x}$. Substituting these values into the formula, we have:

$$ V = \int_{0}^{8} 2\pi x \sqrtTo find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

\[V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, and $f(x)$ is the height of the shell at each x-value.

In this case, the curves intersect at $x = 0$ and $x = 8$, so the integral becomes:

$$V = 2\pi \int_{0}^{8} x \cdot \sqrt{3x} \, dx$$

Simplifying the integrand:

$$V = 2\pi \int_{0}^{8} x^{\frac{To find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

\[ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$ and $b$ are the limits of integration, and $f(x)$ represents the function describing the height of the shell at each point.

For this problem, $a = 0$ and $b = 8$, and $f(x) = \sqrt{3x}$. Substituting these values into the formula, we have:

$$ V = \int_{0}^{8} 2\pi x \sqrt{To find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

\[V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, and $f(x)$ is the height of the shell at each x-value.

In this case, the curves intersect at $x = 0$ and $x = 8$, so the integral becomes:

$$V = 2\pi \int_{0}^{8} x \cdot \sqrt{3x} \, dx$$

Simplifying the integrand:

$$V = 2\pi \int_{0}^{8} x^{\frac{3To find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

\[ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$ and $b$ are the limits of integration, and $f(x)$ represents the function describing the height of the shell at each point.

For this problem, $a = 0$ and $b = 8$, and $f(x) = \sqrt{3x}$. Substituting these values into the formula, we have:

$$ V = \int_{0}^{8} 2\pi x \sqrt{3To find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

\[V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, and $f(x)$ is the height of the shell at each x-value.

In this case, the curves intersect at $x = 0$ and $x = 8$, so the integral becomes:

$$V = 2\pi \int_{0}^{8} x \cdot \sqrt{3x} \, dx$$

Simplifying the integrand:

$$V = 2\pi \int_{0}^{8} x^{\frac{3}{To find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

\[ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$ and $b$ are the limits of integration, and $f(x)$ represents the function describing the height of the shell at each point.

For this problem, $a = 0$ and $b = 8$, and $f(x) = \sqrt{3x}$. Substituting these values into the formula, we have:

$$ V = \int_{0}^{8} 2\pi x \sqrt{3xTo find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

\[V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, and $f(x)$ is the height of the shell at each x-value.

In this case, the curves intersect at $x = 0$ and $x = 8$, so the integral becomes:

$$V = 2\pi \int_{0}^{8} x \cdot \sqrt{3x} \, dx$$

Simplifying the integrand:

$$V = 2\pi \int_{0}^{8} x^{\frac{3}{2To find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

\[ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$ and $b$ are the limits of integration, and $f(x)$ represents the function describing the height of the shell at each point.

For this problem, $a = 0$ and $b = 8$, and $f(x) = \sqrt{3x}$. Substituting these values into the formula, we have:

$$ V = \int_{0}^{8} 2\pi x \sqrt{3x}To find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

\[V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, and $f(x)$ is the height of the shell at each x-value.

In this case, the curves intersect at $x = 0$ and $x = 8$, so the integral becomes:

$$V = 2\pi \int_{0}^{8} x \cdot \sqrt{3x} \, dx$$

Simplifying the integrand:

$$V = 2\pi \int_{0}^{8} x^{\frac{3}{2}} \To find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

\[ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$ and $b$ are the limits of integration, and $f(x)$ represents the function describing the height of the shell at each point.

For this problem, $a = 0$ and $b = 8$, and $f(x) = \sqrt{3x}$. Substituting these values into the formula, we have:

$$ V = \int_{0}^{8} 2\pi x \sqrt{3x} \To find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

\[V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, and $f(x)$ is the height of the shell at each x-value.

In this case, the curves intersect at $x = 0$ and $x = 8$, so the integral becomes:

$$V = 2\pi \int_{0}^{8} x \cdot \sqrt{3x} \, dx$$

Simplifying the integrand:

$$V = 2\pi \int_{0}^{8} x^{\frac{3}{2}} \,To find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

\[ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$ and $b$ are the limits of integration, and $f(x)$ represents the function describing the height of the shell at each point.

For this problem, $a = 0$ and $b = 8$, and $f(x) = \sqrt{3x}$. Substituting these values into the formula, we have:

$$ V = \int_{0}^{8} 2\pi x \sqrt{3x} \,To find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

\[V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, and $f(x)$ is the height of the shell at each x-value.

In this case, the curves intersect at $x = 0$ and $x = 8$, so the integral becomes:

$$V = 2\pi \int_{0}^{8} x \cdot \sqrt{3x} \, dx$$

Simplifying the integrand:

$$V = 2\pi \int_{0}^{8} x^{\frac{3}{2}} \, dxTo find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

\[ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$ and $b$ are the limits of integration, and $f(x)$ represents the function describing the height of the shell at each point.

For this problem, $a = 0$ and $b = 8$, and $f(x) = \sqrt{3x}$. Substituting these values into the formula, we have:

$$ V = \int_{0}^{8} 2\pi x \sqrt{3x} \, dxTo find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

\[V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, and $f(x)$ is the height of the shell at each x-value.

In this case, the curves intersect at $x = 0$ and $x = 8$, so the integral becomes:

$$V = 2\pi \int_{0}^{8} x \cdot \sqrt{3x} \, dx$$

Simplifying the integrand:

$$V = 2\pi \int_{0}^{8} x^{\frac{3}{2}} \, dx\To find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

\[ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$ and $b$ are the limits of integration, and $f(x)$ represents the function describing the height of the shell at each point.

For this problem, $a = 0$ and $b = 8$, and $f(x) = \sqrt{3x}$. Substituting these values into the formula, we have:

$$ V = \int_{0}^{8} 2\pi x \sqrt{3x} \, dx \To find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

\[V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, and $f(x)$ is the height of the shell at each x-value.

In this case, the curves intersect at $x = 0$ and $x = 8$, so the integral becomes:

$$V = 2\pi \int_{0}^{8} x \cdot \sqrt{3x} \, dx$$

Simplifying the integrand:

$$V = 2\pi \int_{0}^{8} x^{\frac{3}{2}} \, dx$$

To find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

$$ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$ and $b$ are the limits of integration, and $f(x)$ represents the function describing the height of the shell at each point.

For this problem, $a = 0$ and $b = 8$, and $f(x) = \sqrt{3x}$. Substituting these values into the formula, we have:

$$ V = \int_{0}^{8} 2\pi x \sqrt{3x} \, dx $$

To find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

$$V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, and $f(x)$ is the height of the shell at each x-value.

In this case, the curves intersect at $x = 0$ and $x = 8$, so the integral becomes:

$$V = 2\pi \int_{0}^{8} x \cdot \sqrt{3x} \, dx$$

Simplifying the integrand:

$$V = 2\pi \int_{0}^{8} x^{\frac{3}{2}} \, dx$$

$$To find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

\[ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$ and $b$ are the limits of integration, and $f(x)$ represents the function describing the height of the shell at each point.

For this problem, $a = 0$ and $b = 8$, and $f(x) = \sqrt{3x}$. Substituting these values into the formula, we have:

$$ V = \int_{0}^{8} 2\pi x \sqrt{3x} \, dx $$

STo find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

$$V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, and $f(x)$ is the height of the shell at each x-value.

In this case, the curves intersect at $x = 0$ and $x = 8$, so the integral becomes:

$$V = 2\pi \int_{0}^{8} x \cdot \sqrt{3x} \, dx$$

Simplifying the integrand:

$$V = 2\pi \int_{0}^{8} x^{\frac{3}{2}} \, dx$$

$$V =To find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

\[ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$ and $b$ are the limits of integration, and $f(x)$ represents the function describing the height of the shell at each point.

For this problem, $a = 0$ and $b = 8$, and $f(x) = \sqrt{3x}$. Substituting these values into the formula, we have:

$$ V = \int_{0}^{8} 2\pi x \sqrt{3x} \, dx $$

SolvingTo find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

$$V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, and $f(x)$ is the height of the shell at each x-value.

In this case, the curves intersect at $x = 0$ and $x = 8$, so the integral becomes:

$$V = 2\pi \int_{0}^{8} x \cdot \sqrt{3x} \, dx$$

Simplifying the integrand:

$$V = 2\pi \int_{0}^{8} x^{\frac{3}{2}} \, dx$$

$$V = To find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

\[ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$ and $b$ are the limits of integration, and $f(x)$ represents the function describing the height of the shell at each point.

For this problem, $a = 0$ and $b = 8$, and $f(x) = \sqrt{3x}$. Substituting these values into the formula, we have:

$$ V = \int_{0}^{8} 2\pi x \sqrt{3x} \, dx $$

Solving thisTo find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

$$V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, and $f(x)$ is the height of the shell at each x-value.

In this case, the curves intersect at $x = 0$ and $x = 8$, so the integral becomes:

$$V = 2\pi \int_{0}^{8} x \cdot \sqrt{3x} \, dx$$

Simplifying the integrand:

$$V = 2\pi \int_{0}^{8} x^{\frac{3}{2}} \, dx$$

$$V = 2To find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

\[ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$ and $b$ are the limits of integration, and $f(x)$ represents the function describing the height of the shell at each point.

For this problem, $a = 0$ and $b = 8$, and $f(x) = \sqrt{3x}$. Substituting these values into the formula, we have:

$$ V = \int_{0}^{8} 2\pi x \sqrt{3x} \, dx $$

Solving this integralTo find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

$$V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, and $f(x)$ is the height of the shell at each x-value.

In this case, the curves intersect at $x = 0$ and $x = 8$, so the integral becomes:

$$V = 2\pi \int_{0}^{8} x \cdot \sqrt{3x} \, dx$$

Simplifying the integrand:

$$V = 2\pi \int_{0}^{8} x^{\frac{3}{2}} \, dx$$

$$V = 2\To find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

\[ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$ and $b$ are the limits of integration, and $f(x)$ represents the function describing the height of the shell at each point.

For this problem, $a = 0$ and $b = 8$, and $f(x) = \sqrt{3x}$. Substituting these values into the formula, we have:

$$ V = \int_{0}^{8} 2\pi x \sqrt{3x} \, dx $$

Solving this integral willTo find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

$$V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, and $f(x)$ is the height of the shell at each x-value.

In this case, the curves intersect at $x = 0$ and $x = 8$, so the integral becomes:

$$V = 2\pi \int_{0}^{8} x \cdot \sqrt{3x} \, dx$$

Simplifying the integrand:

$$V = 2\pi \int_{0}^{8} x^{\frac{3}{2}} \, dx$$

$$V = 2\piTo find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

\[ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$ and $b$ are the limits of integration, and $f(x)$ represents the function describing the height of the shell at each point.

For this problem, $a = 0$ and $b = 8$, and $f(x) = \sqrt{3x}$. Substituting these values into the formula, we have:

$$ V = \int_{0}^{8} 2\pi x \sqrt{3x} \, dx $$

Solving this integral will giveTo find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

$$V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, and $f(x)$ is the height of the shell at each x-value.

In this case, the curves intersect at $x = 0$ and $x = 8$, so the integral becomes:

$$V = 2\pi \int_{0}^{8} x \cdot \sqrt{3x} \, dx$$

Simplifying the integrand:

$$V = 2\pi \int_{0}^{8} x^{\frac{3}{2}} \, dx$$

$$V = 2\pi \To find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

\[ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$ and $b$ are the limits of integration, and $f(x)$ represents the function describing the height of the shell at each point.

For this problem, $a = 0$ and $b = 8$, and $f(x) = \sqrt{3x}$. Substituting these values into the formula, we have:

$$ V = \int_{0}^{8} 2\pi x \sqrt{3x} \, dx $$

Solving this integral will give usTo find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

$$V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, and $f(x)$ is the height of the shell at each x-value.

In this case, the curves intersect at $x = 0$ and $x = 8$, so the integral becomes:

$$V = 2\pi \int_{0}^{8} x \cdot \sqrt{3x} \, dx$$

Simplifying the integrand:

$$V = 2\pi \int_{0}^{8} x^{\frac{3}{2}} \, dx$$

$$V = 2\pi \left[ \To find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

\[ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$ and $b$ are the limits of integration, and $f(x)$ represents the function describing the height of the shell at each point.

For this problem, $a = 0$ and $b = 8$, and $f(x) = \sqrt{3x}$. Substituting these values into the formula, we have:

$$ V = \int_{0}^{8} 2\pi x \sqrt{3x} \, dx $$

Solving this integral will give us the volume ofTo find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

$$V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, and $f(x)$ is the height of the shell at each x-value.

In this case, the curves intersect at $x = 0$ and $x = 8$, so the integral becomes:

$$V = 2\pi \int_{0}^{8} x \cdot \sqrt{3x} \, dx$$

Simplifying the integrand:

$$V = 2\pi \int_{0}^{8} x^{\frac{3}{2}} \, dx$$

$$V = 2\pi \left[ \frac{To find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

\[ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$ and $b$ are the limits of integration, and $f(x)$ represents the function describing the height of the shell at each point.

For this problem, $a = 0$ and $b = 8$, and $f(x) = \sqrt{3x}$. Substituting these values into the formula, we have:

$$ V = \int_{0}^{8} 2\pi x \sqrt{3x} \, dx $$

Solving this integral will give us the volume of the solidTo find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

$$V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, and $f(x)$ is the height of the shell at each x-value.

In this case, the curves intersect at $x = 0$ and $x = 8$, so the integral becomes:

$$V = 2\pi \int_{0}^{8} x \cdot \sqrt{3x} \, dx$$

Simplifying the integrand:

$$V = 2\pi \int_{0}^{8} x^{\frac{3}{2}} \, dx$$

$$V = 2\pi \left[ \frac{2To find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

\[ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$ and $b$ are the limits of integration, and $f(x)$ represents the function describing the height of the shell at each point.

For this problem, $a = 0$ and $b = 8$, and $f(x) = \sqrt{3x}$. Substituting these values into the formula, we have:

$$ V = \int_{0}^{8} 2\pi x \sqrt{3x} \, dx $$

Solving this integral will give us the volume of the solid.To find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

$$V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, and $f(x)$ is the height of the shell at each x-value.

In this case, the curves intersect at $x = 0$ and $x = 8$, so the integral becomes:

$$V = 2\pi \int_{0}^{8} x \cdot \sqrt{3x} \, dx$$

Simplifying the integrand:

$$V = 2\pi \int_{0}^{8} x^{\frac{3}{2}} \, dx$$

$$V = 2\pi \left[ \frac{2}{5To find the volume of the solid generated when the region bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis is rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ can be calculated using the formula:

\[ V = \int_{a}^{b} 2\pi x f(x) \, dx $$

where $a$ and $b$ are the limits of integration, and $f(x)$ represents the function describing the height of the shell at each point.

For this problem, $a = 0$ and $b = 8$, and $f(x) = \sqrt{3x}$. Substituting these values into the formula, we have:

$$ V = \int_{0}^{8} 2\pi x \sqrt{3x} \, dx $$

Solving this integral will give us the volume of the solid.To find the volume of the solid generated when the regions bounded by the graphs of $y = \sqrt{3x}$, $x = 0$, $x = 8$, and the x-axis are rotated about the x-axis, you can use the method of cylindrical shells.

The volume $V$ of the solid is given by the formula:

$$V = 2\pi \int_{a}^{b} x \cdot f(x) \, dx$$

where $a$ and $b$ are the x-values where the curves intersect, and $f(x)$ is the height of the shell at each x-value.

In this case, the curves intersect at $x = 0$ and $x = 8$, so the integral becomes:

$$V = 2\pi \int_{0}^{8} x \cdot \sqrt{3x} \, dx$$

Simplifying the integrand:

$$V = 2\pi \int_{0}^{8} x^{\frac{3}{2}} \, dx$$

$$V = 2\pi \left[ \frac{2}{5}x^{\frac{5}{2}} \right]_{0}^{8}$$

$$V = \frac{4}{5} \pi \cdot 8^{\frac{5}{2}}$$

$$V = \frac{4}{5} \pi \cdot 256$$

$$V = \frac{1024}{5} \pi$$

So, the volume of the solid is $\frac{1024}{5} \pi$ cubic units.