# How do you find the volume bounded by #x-8y=0# & the lines #x+2y# revolved about the y-axis?

Volume of revolution =

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To find the volume bounded by (x - 8y = 0) and the lines (x + 2y) revolved about the y-axis, you can use the method of cylindrical shells.

- Solve for the intersection point of the two curves by setting (x - 8y = x + 2y) and solving for (x) and (y).
- Integrate the volume element formula (\int 2\pi x h , dx) where (h) is the height of the shell, which is the difference between the curves at a given (x) value.
- The limits of integration will be from the x-coordinate of the intersection point to the x-coordinate where the curve (x + 2y) intersects the y-axis.
- Integrate the formula with respect to (x) over the specified limits to find the total volume.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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