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Chapter 9: Q. 40 (page 775)

Areas of regions bounded by polar functions: Find the areas of the following regions. The area inside both polar roses r=sin3胃andr=cos3胃.

Short Answer

Expert verified

The area inside both polar roses is16-2-26units

Step by step solution

01

Given information

r=sin3胃andr=cos3胃

02

Area

The graph of both the curves is,

The limits of the integration is,

sin3胃=cos3胃鈬�tan3胃=1鈬�3胃=蟺4鈬�胃=蟺12

The area bounded by both the curves is,

A=12鈭�伪尾r2d胃A=3脳12鈭�0蟺12sin3胃d胃A=12-cos3胃30蟺8A=12-cos3蟺83+cos303A=16-2-26units

The required area isA=16-2-26units

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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=41+sin胃

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

0,2

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鈭�0蟺(1+cos胃)2d胃

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

x=0

Use Cartesian coordinates to express the equations for the hyperbolas determined by the conditions specified in Exercises 38鈥�43.

foci(卤2,0), directricesx=卤1
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