The region in the first quadrant bounded by the -axis

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

Problem

The region in the first quadrant bounded by the

y

-axis, the line

y=3

, and the curve

x=y^{2}

is the base of a solid. Cross sections perpendicular to the

y

-axis satisfy • for

0\le y\le 1

, the cross section is a square whose side length equals

x=y^{2}

; • for

1<y\le 3

, the cross section is an equilateral triangle whose base length equals

x=y^{2}

. Determine the volume of the solid.