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Chapter 9: Q. 26 (page 756)

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=胃for0鈮�胃鈮�2蟺

Short Answer

Expert verified

The integral can be given as 鈭�02蟺1+胃2d胃and its length is21.25units

Step by step solution

01

Given information

We are given a spiral represented by a functionr=胃for0鈮�胃鈮�2蟺

02

We find the definite integral and evaluate it

We know that length of polar curve can be given as

鈭�ab(f(胃))2+(f'(胃))2d胃

We are given r=胃drd胃=1

Substituting the above values in the integral we get,

鈭�02蟺1+胃2d胃

On solving the integral we get the value as

role="math" localid="1649471467926" 鈭�02蟺1+胃2d胃=21.25units

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Most popular questions from this chapter

Each of the integrals or integral expressions in Exercises 38-44represents the area of a region in the plane. Use polar coordinates to sketch the region and evaluate the expressions.

role="math" localid="1649518287481" 3鈭�0蟺/2sin23胃d胃.

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

y=-3

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

3,4

Complete example 2 by evaluating the integral expression

鈭�02蟺3(12+cos胃)2d胃-鈭�蟺4蟺3(12+cos胃)2d胃

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

r=11-cos胃
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