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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 is

A=-π4π2(22+sinθ)2dθ--π2-π4(22+sinθ)2dθ

Short Answer

Expert verified

The value of the integral is 1.0707 units

Step by step solution

01

Given information

We are given the integral asA=-π4π2(22+sinθ)2dθ--π2-π4(22+sinθ)2dθ

02

Plot the graph of the function

Using graphing utility we have,

03

Evaluate the integral

We have,

A=-π4π2(22+sinθ)2dθ--π2-π4(22+sinθ)2dθA=-π4π2(12+2sinθ+sin2θ)dθ--π2-π4(12+2sinθ+sin2θ)dθNowusingCAScalculatorwegetA=1.0707units

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