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=0

x=4

. For

0\le x\le 2

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

3x+1

units. For

2\le x\le 4

, each cross section is a rectangle whose height is

2

units and whose width is

x+1

units. Calculate the exact volume of the solid.