Question

just help me set it up and I'll solve it :)

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis.

y=x^2, y=0, x=2, about the y-axis

Answer 1

If you visualize the graph of y (where y=0 and x=2 are boundaries), you will see that its domain is in the first quadrant from y = 0 to 4. We need it in terms of y if we want to use the disc method, so x = sqrt{y}.
Therefore integrate
\[\pi \int\limits_{0}^{4}(\sqrt{y})dy\]

Answer 2

I got 12pi?

Answer 3

I had 16pi/3

Answer 4

nope thats wrong... mine is too

Answer 5

I forgot to square the radius. Integrate y.

Answer 6

pi(y^2/2) from 0 to 4

Answer 7

8pi