# How do you find the volume of the solid bounded by #x=y^2# and the line #x=4# rotated about the x axis?

By signing up, you agree to our Terms of Service and Privacy Policy

To find the volume of the solid bounded by (x = y^2) and the line (x = 4) rotated about the x-axis, you can use the method of cylindrical shells.

The volume (V) is given by the integral:

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

Where:

- (a) and (b) are the x-values where the curves intersect,
- (f(x)) is the height of the shell, and
- (x) represents the radius of the shell.

In this case, the bounds of integration are from (x = 0) to (x = 4) (the intersection points of (x = y^2) and (x = 4)). (f(x)) represents the distance between the curve (x = y^2) and the line (x = 4), which is (4 - x). The radius (x) represents the distance from the axis of rotation to the shell.

So, the integral becomes:

[ V = \int_{0}^{4} 2\pi x (4 - x) ,dx ]

You can solve this integral to find the volume of the solid.

By signing up, you agree to our Terms of Service and Privacy Policy

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.

- How do you find the arc length of the curve #y=1+6x^(3/2)# over the interval [0, 1]?
- What is the surface area of the solid created by revolving #f(x) = 3x, x in [2,5]# around the x axis?
- What is the arclength of #f(x)=sqrt(x^2-1)/x# on #x in [-2,-1]#?
- How do you find the surface area of a solid of revolution?
- How can I solve this differential equation? : #(2x^3-y)dx+xdy=0#

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7