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Chapter 13: Q.2 (page 1025)

Each of the integral expressions that follow represents the area of a region in the plane bounded by a function expressed in polar coordinates. Use the ideas from this section and from Chapter 9 to sketch the regions, and then evaluate each integral

4鈭�0蟺4COS22胃d胃

Short Answer

Expert verified

The value of the integral is蟺2square unit

Step by step solution

01

Step 1. Given information

Integral:

4鈭�0蟺4COS22胃d胃
02

 Step 2. Plot the curve 

Since the area of a function is r=f(胃)is12鈭�abr2d胃

So by comparing the given integral we get,

r=22cos2胃

So the graph of this curve is:

03

Step 3. Evaluate integral

4鈭�0蟺4cos22胃d胃=4鈭�0蟺41+cos4胃2d胃=2鈭�0蟺41+cos4胃d胃=2胃+sin4胃40蟺4=2蟺4+蝉颈苍蟺4-0=2蟺4-0=蟺2

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