Well, if you graph things, you have a curved triangular region with vertices at (-2,8),(-2,0),(0,0).
So, using shells of thickness dx, you have the area as
∫[-2,0] 2πrh dx
where
r = 1-x
h = y = -x^3
using washers of thickness dy, you have
∫[0,8] π(R^2-r^2) dy
where
R = 1+2
r = 1+x = 1+∛y
find the volume generated by revolving the area bounded by y=-x^3, y=0, and x=-2 about the line x=1.
I know how to the solve the problem but am not sure how to get the interval. Please help.
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