Find the volume of the solid obtained by rotating the region bounded by y=x and y=√x about the line x=2.

Question

Volume =

Answer 1

intersection:
√x = x
x = x^2
x = 0 or x = 1

V = π∫ (2-√x)^2 - (2-x)^2 dy from y = 0 to 1
expand, integrate, etc

Answer 2

Now, you may be asking yourself, "Self, how can I integrate
∫ (2-√x)^2 dy ?"
You just need to express x as a function of y. That makes the volume
v = π∫[0,1] (2-y^2)^2 - (2-y)^2 dy = 8π/15

Answer 3

Thanks for the correction, oobleck