Let be the region in the first quadrant bounded by ,

MATHEMATICS · Multi-part · AP · Calculus AB · Applications of Integration · Applications of Integration

Problem

Let

R

be the region in the first quadrant bounded by

x=\sqrt{y}

x=y^{2}

, and

y=1

. The region

R

is revolved about the

y

–axis to form a solid. (a) Find all

y

–values where

x=\sqrt{y}

and

x=y^{2}

intersect. (b) For

0\le y\le1

, determine which curve lies farther from the

y

–axis. Justify your answer. (c) Write an integral expression representing the volume of the solid generated by revolving

R

about the

y

–axis. (d) Evaluate the integral from part (c) and state the exact volume of the solid.