Volume With Known Cross Sections

Question

The base of a solid is the region enclosed by the graphs of $$ y = \sqrt{x} $$ and $$ y = x^2 $$. For this solid, cross sections perpendicular to the y-axis are isosceles right triangles with a leg in the base. Which of the following expressions gives the volume of the solid?

Accepted Answer

$$ \frac{1}{2} \int_0^1 (\sqrt{y} - y^2)^2 \, dy $$

Answer

$$ \frac{1}{4} \int_0^1 (\sqrt{y} - y^2)^2 \, dy $$

Answer

$$ \int_0^1 (\sqrt{y} - y^2)^2 \, dy $$

Answer

$$ \frac{1}{2} \int_0^1 (\sqrt{x} - x^2)^2 \, dx $$

Volume With Known Cross Sections

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