Region S is bounded by and for

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

Problem

Region S is bounded by

y=x

and

y=x^{2}

for

0\le x\le1

. Revolve S about the line

x=3

. Write, but do not evaluate, the definite integral that represents the volume (i) using

x

as the variable of integration and (ii) using

y

as the variable of integration.