Single Variable Calculus

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Single Variable Calculus, Chapter 6, 6.2, Section 6.2, Problem 24

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Find the value generated by rotating $\mathscr{R}_2$ about $OC$

If you rotate $\mathscr{R}_2$ about $OC$, by using horizontal strip, you will form a disk with radius $y^2$. Thus, the cross sectional area can be computed as $A(y) = \pi(y^2)^2$. Therefore, the value is...

$ \begin{equation} \begin{aligned} V &= \int^1_0 \pi y^4 dy\\ \\ V &= \pi \left[ \frac{y^5}{5} \right]^1_0\\ \\ V &= \frac{\pi}{5} \text{ cubic units} \end{aligned} \end{equation} $

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