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Q. 41

Expert-verified

Calculus

Found in: Page 756

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 $A = \int_{0}^{\frac{π}{2}} \sin 2 θ d θ$

The area is 1 units

The graph can be given as

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given information

We are given an integral representing area as $A = \int_{0}^{\frac{π}{2}} \sin 2 θ d θ$

Step 2: Sketch the graph

On comparing with standard equation we get,

$r = \sqrt{\sin 2 θ}$

Using graphing utility we get,

Step 3: Evaluate

We are given $A = \int_{0}^{\frac{π}{2}} \sin 2 θ d θ$

Using CAS calculator we get,

$A = 1 u n i t$

Most popular questions for Math Textbooks

Use Cartesian coordinates to express the equations for the parabolas determined by the conditions specified in Exercises 22–31.

$directrix x = x_{0}, focus (x_{1}, y_{1}), where x_{0} \neq x_{1}$ .

Use Cartesian coordinates to express the equations for the parabolas determined by the conditions specified in Exercises 22–31.

$r = \frac{3}{1 + \cos θ}$

in exercise 31-36 find a definite integral that represents the length of the specified polar curve, and then use graphing calculator or computer algebra system to approximate the value of integral

The limacon $r = 2 + \cos θ$

Use Cartesian coordinates to express the equations for the parabolas determined by the conditions specified in Exercises 22–31.

$directrix y = 0, focus (0, 1)$

In Exercises 32–47 convert the equations given in polar coordinates to rectangular coordinates.
$θ = \frac{7 π}{6}$

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