Question

Find the volume of the solid generated by revolving the region bounded by the given curves about the x-axis.

y=x^2+1
x+y=3


Please help me set up the integral!

Answer 1

First you need their intersection, that should be easy
Hope you get (-2,5) and (1,2)
The outer radius is (3-x)
the inner radius is (x^2+1)

so you want ∫ ( (3-x)^2 - (x^2+1)^2 )dx from x = -2 to 1

expand and the rest is pretty straightforward.
Let me know what you get

Answer 2

Awesome, that's what I got!