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Chapter 9: Q. 37 (page 775)

Areas of regions bounded by polar functions: Find the areas of the following regions. The area bounded by one loop of r2=鈭�sin2胃

Short Answer

Expert verified

The required area is34units

Step by step solution

01

Given information

r2=鈭�sin2胃

02

Area

The graph of the given function r2=鈭�sin2胃is,

The area bounded by one loop is,

A=12鈭�伪尾r2d胃A=12鈭�0蟺2-sin2胃d胃A=12cos2胃20蟺2A=12cos2蟺22-cos20A=12-12-1A=34units

The required area isA=34units

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Most popular questions from this chapter

Consider the hyperbola with equation x2A2-y2B2=1.Let F be the focus with coordinates (A2+B2,0).Let e=A2+B2A and l be the vertical line with equation x=Ae. Show that for any point P on the hyperbola, FPDP=e,where D is the point on l closest to P.

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

foci(卤伪,0), major axis4伪

In Exercises 32鈥�47 convert the equations given in polar coordinates to rectangular coordinates.

r=-3sec胃

In Exercises 24鈥�31 find all polar coordinate representations for the point given in rectangular coordinates.

-2,0

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
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