009B Sample Final 1, Problem 5

The region bounded by the parabola $y=x^{2}$ and the line $y=2x$ in the first quadrant is revolved about the $y$ -axis to generate a solid.

(a) Sketch the region bounded by the given functions and find their points of intersection.

(b) Set up the integral for the volume of the solid.

(c) Find the volume of the solid by computing the integral.

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