Consider the region enclosed by the graphs of and on the interval

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

Problem

Consider the region enclosed by the graphs of

y = x

and

y = 2 - x

on the interval

0 \le x \le 2

. This region is revolved about the horizontal line

y = 3

to create a solid of revolution. Determine the

x

–coordinate at which the definite integral for the volume must be split, and in one sentence explain why the split is required.