A solid has base region in the first quadrant bounded above by the piecewise curve…

MATHEMATICS · Subjective · AP · Calculus AB · Applications of Integration · Applications of Integration

Problem

A solid has base region

S

in the first quadrant bounded above by the piecewise curve

y=\begin{cases}x,&0\leq x\leq1\\\sqrt{x},&1<x\leq4\end{cases}

and below by the

x

-axis. Cross sections perpendicular to the

x

-axis are rectangles whose height is three times their base width. Find the exact volume of the solid.