Mathematics

Problem

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

y=\sqrt{x}

and below by the x-axis on the interval

0\le x\le 4

. Cross-sections perpendicular to the x-axis are rectangles whose height at

x

x+1

. What is the volume of the solid? a)

\dfrac{256}{15}

\dfrac{272}{15}

\dfrac{136}{15}

\dfrac{440}{15}