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Chapter 9: Q. 46 (page 756)

Use Theorem 9.13 to show that the area of the circle defined by the polar equationr=2acos胃is蟺a2.

Short Answer

Expert verified

The area of the circle is蟺a2.

Step by step solution

01

Step 1. Given Information

The circle is bounded by the curve r=2acos胃.

02

Step 2. Use the formula for area of a region bounded by a curve 

  • The region is bounded by the curve r=2acos胃.
  • The region is a circle, so the boundary arcs will be 胃=0to胃=2蟺.
  • But the curve is traced twice in this region.
  • So, the area of the region will be calculated as follows:

12脳12鈭�02蟺4a2cos2胃d胃=a2鈭�02蟺cos2胃d胃=a2鈭�02蟺1+cos2胃2d胃=a2脳12鈭�02蟺1d胃+鈭�02蟺cos2胃d胃=12a22蟺+0=蟺a2

  • Hence, the area of the curve is 蟺a2.

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Most popular questions from this chapter

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

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