A solid has a base in the –plane bounded above by the curve

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

Problem

A solid has a base in the

xy

–plane bounded above by the curve

y=\sqrt{x}

, bounded below by the

x

–axis, and bounded on the left by the

y

–axis. Cross sections taken perpendicular to the

x

–axis are squares. The volume of the solid is exactly

10

cubic units. (a) Express the volume

V

of the solid as a function of the unknown right‐hand boundary point

b\,(>0)

, where

x

ranges from

0

b

. Do not evaluate the integral. (b) Determine the value of

b

that yields a volume of

10

cubic units. Give the exact value or a decimal approximation accurate to three decimal places.