The curves and enclose a region in the first quadrant

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

Problem

The curves

x=y

and

x=y^{2}

enclose a region in the first quadrant. For every

y

in this region, a cross section perpendicular to the

y

-axis is a right triangle whose altitude is twice its base (which lies in the region). Compute the volume of the resulting solid.