For the region bounded by and on

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

Problem

For the region bounded by

y = x^{2}

and

y = x + 1

0 \le x \le 3

, determine the

x

-value at which the set of cross sections formed by revolving the region about the

x

-axis changes its outer radius. Briefly explain why the definite integral representing the volume must be split at this point.