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Chapter 9: Q. 38 (page 775)

Areas of regions bounded by polar functions: Find the areas of the following regions. The area bounded by one loop of r2=4cos2胃.

Short Answer

Expert verified

The area bounded by one loop is2units

Step by step solution

01

Given information

r2=4cos2胃

02

Area

The graph of the given function is,

The area bounded by one loop is,

A=12鈭�伪尾r2d胃A=12鈭�-蟺4蟺44cos2胃d胃A=2sin2胃2-蟺4蟺4A=2sin2蟺42-sin2-蟺42A=412+12A=2units

The required area isA=2units

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Most popular questions from this chapter

Use Cartesian coordinates to express the equations for the parabolas determined by the conditions specified in Exercises 22鈥�31.

r=伪1+sin胃

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

r=11-cos胃

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

y=-3

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

r=e胃for2k蟺鈮�胃鈮�2(k+1)蟺

Use Cartesian coordinates to express the equations for the ellipses determined by the conditions specified in Exercises 32鈥�37.

foci(卤1,0),major axis4
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