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# Use the integration capabilities of the graphing utility to approximate the volume of the solid generated by revolving the region about the y-axis.$y=\sqrt{1-x^3}, \quad y=0, \quad x=0$

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b.

$V=2\pi \int_a^b p\left(x\right)h\left(x\right)dx$

\begin{aligned} V&=2\pi \int_a^b p\left(x\right)h\left(x\right)dx && \text{Apply Shell method.} \\ &=2\pi \int_0^1 x\sqrt{1-x^3} dx && \text{Substitute} \ x \ \text{for} \ p\left(x\right) \ \text{and} \ \sqrt{1-x^3} \ \text{for} \ h\left(x\right). \\ &\approx 2\pi \cdot 0.37 && \text{Use the IntegralCalculator.} \\ &\approx 2.32 \end{aligned}

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