Volume With Rectangular Cross Sections
The region enclosed by the graphs of $$ y = x^3 $$ and $$ y = x $$ is the base of a solid. For this solid, cross sections perpendicular to the y-axis are rectangles whose height is twice the length of their base in the xy-plane. Which of the following expressions gives the volume of the solid?
A
$$ 2 \int_0^1 (x - x^3)^2 \, dx $$
B
$$ \int_0^1 (y - y^{1/3})^2 \, dy $$
C
$$ 2 \int_0^1 (y + y^{1/3})^2 \, dy $$
D
$$ 2 \int_0^1 (y - y^{1/3})^2 \, dy $$
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