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Answers without the blur. Sign up and see all textbooks for free! Q. 41

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

Book edition 1st
Author(s) Peter Kohn, Laura Taalman
Pages 1155 pages
ISBN 9781429241861 # Each of the integral in exercise 38-44 represents the area of a region in a plane use polar coordinates to sketch the region and evaluate the expression The integral is $A={\int }_{0}^{\frac{\pi }{2}}\mathrm{sin}2\theta d\theta$

The area is 1 units

The graph can be given as See the step by step solution

## Step 1: Given information

We are given an integral representing area as $A={\int }_{0}^{\frac{\pi }{2}}\mathrm{sin}2\theta d\theta$

## Step 2: Sketch the graph

On comparing with standard equation we get,

$r=\sqrt{\mathrm{sin}2\theta }$

Using graphing utility we get, ## Step 3: Evaluate

We are given $A={\int }_{0}^{\frac{\pi }{2}}\mathrm{sin}2\theta d\theta$

Using CAS calculator we get,

$A=1unit$ ### Want to see more solutions like these? 