Let T be the region in the first quadrant bounded by and

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

Problem

Let T be the region in the first quadrant bounded by

y=2x - x^{2}

and

y=0

. Revolve T about the line

y=3

. Express the volume of the resulting solid as a definite integral in two different ways: one with respect to

x

and the other with respect to

y

. Do not evaluate either integral.