# How do you use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region #x=y^2#, #y=0#, and #y=sqr2# rotated about the x axis?

It's unclear what your solid is, but the only one that makes sense is

You only need the positive one since

Since the shell method implies you are rotating about the y-axis (which is inconvenient for the regular revolution method), we can rewrite this for that.

Now we really just have

The shell method is:

where:

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 solve the initial-value problem #y'=sinx/siny# where #y(0)=π/4#?
- What is the logistic model of population growth?
- Show that # y^2 = (4x)(a-x) = 4ax-4x^2 # is a solution to the DE? # 2xy dy/dx = y^2 - 4x^2#
- How do you find the arc length of the curve #y=lnx# over the interval [1,2]?
- How do you use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by #y^2=8x# and x=2 revolved about the x=4?

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