Problem

Each integral represents the volume of a solid. D…

00:23

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.

More Answers

01:26

Wen Z.

Topics

Applications of Integration

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 6

Applications of Integration

Section 2

Volumes

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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.

Amrita B.

Topics

Applications of Integration

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 6

Applications of Integration

Section 2

Volumes

Top Calculus 2 / BC Educators

Catherine R.

Missouri State University

Caleb E.

Baylor University

Kristen K.

University of Michigan - Ann Arbor

Samuel H.

University of Nottingham