Volumes of Revolution (College Board AP® Calculus AB)

Exam Questions

23 mins10 questions

1 mark

A region in the first quadrant is enclosed by the graphs of $y = x^{3}$ and $y = \sqrt{x}$ . If the region is rotated about the $x$ -axis, which of the following represents the volume of the solid that is generated?

$\begin{array}{rcl} \int_{0}^{1} (\sqrt{x} - x^{3}) d x \end{array}$
$\begin{array}{rcl} \int_{0}^{1} π {(\sqrt{x} - x^{3})}^{2} d x \end{array}$
$\begin{array}{rcl} \int_{0}^{1} π x (1 - x^{5}) d x \end{array}$
$\begin{array}{rcl} \int_{0}^{1} π x^{\frac{7}{2}} d x \end{array}$

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