Book edition 1st

Author(s) Peter Kohn, Laura Taalman

Pages 1155 pages

ISBN 9781429241861

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Short Answer

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 $\frac{1}{2} \int_{0}^{2 π} {(1 + \sin θ)}^{2} d θ$

The value of integral is 4.71 units

The graph can be given as

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given information

We are given an integral $\frac{1}{2} \int_{0}^{2 π} {(1 + \sin θ)}^{2} d θ$

Step 2: Sketch the function

Comparing with standard equation we get $r = 1 + \sin θ$

Using graphing utility we get

Step 3: Evaluate the integral

We get,

$A = \frac{1}{2} \int_{0}^{2 π} {(1 + \sin θ)}^{2} d θ A = \frac{1}{2} \int_{0}^{2 π} (1 + 2 \sin θ + \sin^{2} θ) d θ A = 4.71 u n i t s$

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Calculus

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Short Answer

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 $\frac{1}{2} \int_{0}^{2 π} {(1 + \sin θ)}^{2} d θ$

Step by Step Solution

Step 1: Given information

Step 2: Sketch the function

Step 3: Evaluate the integral

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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 expressionThe integral is 12∫02π(1+sinθ)2dθ

Step by Step Solution

Step 1: Given information

Step 2: Sketch the function

Step 3: Evaluate the integral

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Pure Maths

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 $\frac{1}{2} \int_{0}^{2 π} {(1 + \sin θ)}^{2} d θ$