Find the volume bounded by r=2-2cos theta and r=-6cos theta
Would this be right
1/2 ∫ [5π/3,π/3] ((-6cos theta)^2 - (2-2cos theta)^2) dtheta
Not quite. The curves intersect at (±2π/3,3)
Also, you need an interval inside both curves.
Take a look at
https://www.desmos.com/calculator/ms3eghkkgz
Now the nasty thing about these curves is that pesky -6cosθ. While it marks the right intersection points, θ doesn't line up. Try using some other intervals on that graph, and you can see the difficulty.