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Chapter 9: Q. 38 (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 is12鈭�02蟺(1+sin胃)2d胃

Short Answer

Expert verified

The value of integral is 4.71 units

The graph can be given as

Step by step solution

01

Given information

We are given an integral12鈭�02蟺(1+sin胃)2d胃

02

Sketch the function

Comparing with standard equation we get r=1+sin胃

Using graphing utility we get

03

Evaluate the integral

We get,

A=12鈭�02蟺(1+sin胃)2d胃A=12鈭�02蟺(1+2sin胃+sin2胃)d胃A=4.71units

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Most popular questions from this chapter

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

r=24+cos胃

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

y=-3

Sketch the graphs of the equations

r=22+cos胃and localid="1649860998050" r=22+sin胃

What is the relationship between these graphs? What is the eccentricity of each graph?

Find a definite integral expression that represents the area of the given region in polar plane and then find the exact value of the expression

The region inside the circlex2+y2=1andrightoftheverticallinex=12

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

6,23
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