A solid extends along the x-axis from to

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

Problem

A solid extends along the x-axis from

x=1

x=7

. For

1\le x\le 4

, each cross section perpendicular to the x-axis is a square whose side length is

\sqrt{x}

units. For

4\le x\le 7

, each cross section is a rectangle whose height is

\dfrac{x}{2}

units and whose width is

3

units. Compute the exact volume of the solid.