Question

http://prntscr.com/a5szf7

Answer 1

Since I'm doing this in terms of y, does cos(2x) become x/cos2?

Answer 2

You're rotating about the x-axis,
so you would like to integrate in x,

When the subject of your integral matches the axis of spin,
you get disks/washers.

Answer 3

So you want it in terms of x, yes?

Answer 4

oh yes, I wasn't paying attention to the question

Answer 5

You COULD integrate in y,
but it would be pretty difficult with what you've learned so far.\[\large\rm y=\cos(2x)\qquad\qquad\to\qquad\qquad x=\frac{1}{2}\arccos(y)\]That function is a little more difficult to integrate :)