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Expert-verified Found in: Page 756 ### Calculus

Book edition 1st
Author(s) Peter Kohn, Laura Taalman
Pages 1155 pages
ISBN 9781429241861 # Find a definite integral expression that represents the area of the given region in the polar plane and then find the exact value of expressionThe region bounded enclosed by the spiral $r=\theta$ and the x-axis on the interval $0\le \theta \le \pi$

The integral can be given as $\frac{1}{2}{\int }_{0}^{\pi }{\theta }^{2}d\theta$. The exact value of integral can be given as 5.165 units

See the step by step solution

## Step 1: Given information

We are given an equation of spiral as $r=\theta$

## Step 2: Evaluate

The area can be given as

$A=\frac{1}{2}{\int }_{0}^{\pi }{r}^{2}d\theta \phantom{\rule{0ex}{0ex}}A=\frac{1}{2}{\int }_{0}^{\pi }{\theta }^{2}d\theta \phantom{\rule{0ex}{0ex}}A=\frac{1}{2}\left(10.33\right)\phantom{\rule{0ex}{0ex}}A=5.165unit$ ### Want to see more solutions like these? 