AP Calculus AB Cha 5 C Calculate Volumes of Solids of Revolution Using Definite Integrals Questions

Practise cross-sectional-volume questions by translating geometric area formulas into an integral for volume.

Exam points

The graph above represents the curve C, given by $f(x)=\frac{6}{\sqrt[3]{2 x+5}}$ for $-2 \leq x \leq 11$ .

Set up, but do not evaluate, an integral for the volume of the solid generated when R is rotated around the x-axis.

Then

\begin{aligned} \Delta V & =\pi r^{2} \Delta x=\pi y^{2} \Delta x=\pi\left(\frac{6}{\sqrt[3]{2 x+5}}\right)^{2} \Delta x, \text { so } \\ V & =\pi \int_{-2}^{11} \frac{36}{(2 x+5)^{2 / 3}} d x \end{aligned}

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