Question

Consider the solid obtained by rotating the region bounded by the given curves about the line x = -3.
y = x^2 , x = y^2

Find the volume V of this solid.
I keep finding the wrong answer.

Answer 1

The two parabolas enclose an area between (0,0) and (1,1)
y = x^2 or x=sqrt y is on the right and lower there.
y = x^(1/2) or x = y^2 is above and left there. (All in quadrant one, no worry about signs )
the radius to x = -3 is (3+x)
so outer radius = 3 + sqrt y
inner radius = 3 + y^2
find outer volume
pi (3+y^.5)^2 dy from 0 to 1
find inner volume
pi (3+y^2)^2 dy from 0 to 1
subtract