Question

I'm trying to calculate the volume of
y = 2-x^(2)
y = x^(2)
Rotated around x=1
using shells but I keep getting an integral that gives me zero

Answer 1

\[\int\limits_{-1}^{1} 2pi(x)(2-x^{2} - x^{2})dx = 0\]

Answer 2

the height being
(2−x2−x2)

am I incorrect that the radius is x?

Answer 3

This being the picture of the solid and shell

Answer 4

yep.. your radius should be 1-x

Answer 5

why is that if I may ask?

Answer 6

the distance from your rotation axis to the representative rectangle with width dx is 1- the x-coordinate. so r=1-x