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Chapter 10: Q. 23 (page 777)

The arc length of polar functions: Find the arc lengths of the following polar functions.

r=a, where ais a positive constant, for 胃鈭�[0,2蟺]

Short Answer

Expert verified

The arc length is 2a蟺units

Step by step solution

01

Given information.

The curve r=aand胃鈭�0,2蟺.

02

Length of an arc.

The length of an arc is given by:

L=鈭�伪尾r2+drd胃2d胃

So,

L=鈭�02蟺a2+02d胃鈭�dad胃=0=鈭�02蟺a2d胃=鈭�02蟺ad胃=2a蟺-0=2补蟺

03

Step 3:  Conclusion.

The arc length of the given polar is2a蟺units.

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