Find the volume of the solid obtained by rotating the region bounded by y=x and y=√x about the line x=3

Answer 1

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Answer 2

I'm assuming we are rotating the area from x = 0 to 1 around x = 3

The area is the integral for x from 0 to 1 of (sqrt(x)-x)dx

The volume of the revolved area is the integral for x from 0 to 1 of (sqrt(x)-x)(2π(3-x))dx

where 3-x is the rotational radius.

You can multiply out the integrand and all the terms follow the power rule.

2π x integral from 0 to 1 of (3x^1/2- 3x - x^3/2 + x²)dx

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