Integration Volume: Finding the Rotation of Shaded Area

[thereddevils]

Homework Statement

Find the volume of solid generated when the shaded area is rotated through pi radians about the y-axis . The graphs are y=x^2 and y=2-x^2 .

Homework Equations

The Attempt at a Solution

i did everything and found the answer to be 16/15 pi but the answer given is pi .

$$V=\pi \int^{1}_{0}x^4 dx+\pi \int^{2}_{1}(2-x^2)^2 dx$$

any mistakes in my set up ?

 

[phyzguy]

When I set it up, I got:

$$V=\int_0^1\pi x\int_{x^2}^{2-x^2} dy dx = \int_0^1\pi x(2-2x^2)dx = 2\pi[\frac{x^2}{2}-\frac{x^4}{4}]_0^1 = \frac{\pi}{2}$$

However, this gives pi/2, not pi. Are you sure pi is the right answer? Anyone else?

 

[thereddevils]

ok , i think i see my mistake , its with respect to y .