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Chapter 9: Q. 35 (page 775)

Areas of regions bounded by polar functions: Find the areas of the following regions.

The area bounded by r=1鈭�sin胃

Short Answer

Expert verified

The area bounded by the function isA=蟺unit2

Step by step solution

01

Given information

Given curve isr=1鈭�sin胃

02

Area

The area bounded by the curve is,

A=12鈭�伪尾r2d胃A=12鈭�02蟺1-sin胃2d胃A=12鈭�02蟺1+sin2胃-2sin胃d胃A=12鈭�02蟺3-cos2胃2-2sin胃d胃A=123胃2-sin2胃4+2cos胃02蟺A=126蟺3-sin4蟺4+2cos2蟺-0+2cos0A=122蟺-0+2-2A=蟺unit2

The area bounded by the function isA=蟺unit2

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Most popular questions from this chapter

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

r=24+sin胃

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

1,0

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

r=tan胃

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

The spiralr=胃for0鈮�胃鈮�2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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