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Numerade Educator

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Problem 39 Medium Difficulty

Each integral represents the volume of a solid. Describe the solid.

$ \pi \displaystyle \int_{0}^\pi \sin x dx $

Answer

$\pi \int_{0}^{\pi} \sin x d x=\pi \int_{0}^{\pi}(\sqrt{\sin x})^{2} d x$ describes the volume of solid obtained by rotating the region
$g=\{(x, y) | 0 \leq x \leq \pi, 0 \leq y \leq \sqrt{\sin x}\}$ of the $x y$ -plane about the $x$ -axis.

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Video Transcript

okay for this problem? Using the formula V is pi Times intro from A to B of R squared DX. We know that our our is square of sign acts. Therefore, we know we're looking at the region bounded by why is skirt of sign acts like this And then we'll call the fact that why zero X is between zero and pi and inclusive of either of them and we know it's rotated about the X axis.