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Chapter 9: Q. 40 (page 756)

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 isA=鈭�-蟺2蟺2(2-sin胃)2d胃

Short Answer

Expert verified

The area is 14.137units

The sketch can be given as

Step by step solution

01

Given information

We are given a integralA=鈭�-蟺2蟺2(2-sin胃)2d胃

02

Sketch the graph

Using the standard formula we get, r=2-sin胃

using graphing utility we get,

03

Evaluate

We have,

A=鈭�-蟺2蟺2(2-sin胃)2d胃UsingCAScalculatorweget,A=14.137units

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Most popular questions from this chapter

In Exercises 24鈥�31 find all polar coordinate representations for the point given in rectangular coordinates.

0,-3

In exercise 26-30 Find a definite integral that represents the length of the specified polar curve and then find the exact value of integral

the spiralr=e胃for0鈮�胃鈮�2蟺

Use polar coordinates to graph the conics in Exercises 44鈥�51.

r=21+cos胃

In exercise 26-30 Find a definite integral that represents the length of the specified polar curve and then find the exact value of integral

r=e胃for2k蟺鈮�胃鈮�2(k+1)蟺

In Exercises 48鈥�55 convert the equations given in rectangular coordinates to equations in polar coordinates.

x=4
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