A solid has its base in the plane given by the region enclosed by and

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

Problem

A solid has its base in the plane given by the region enclosed by

y = x^2

and

y = 4

. For each

x

between the points of intersection, the cross section perpendicular to the

x

-axis is a rectangle whose height is three times the length of its base. Provide a definite integral in terms of

x

that represents the volume of the solid; do not evaluate.