APFIVE Volume With Known Cross Sections
Let R be the region enclosed by the graphs of $$y = \sqrt{x}$$ and $$y = x^2$$. Region R is the base of a solid. For this solid, each cross section perpendicular to the y-axis is an isosceles right triangle with the length of each leg equal to the width of R at that y-value. Which of the following integrals gives the volume of the solid?
A
$$ \int_0^1 (\sqrt{y} - y^2)^2 \, dy $$
B
$$ \frac{1}{2} \int_0^1 (\sqrt{y} - y^2)^2 \, dy $$
C
$$ \frac{1}{4} \int_0^1 (\sqrt{y} - y^2)^2 \, dy $$
D
$$ \frac{1}{2} \int_0^1 (\sqrt{x} - x^2)^2 \, dx $$
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