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Chapter 9: Q. 31 (page 775)

Areas of regions bounded by polar functions: Find the areas of the following regions. The area bounded by the function r=a, where a is a positive constant.

Short Answer

Expert verified

The area bounded by the function is4蟺36unit2

Step by step solution

01

Given information

The function isr=a, whereais a positive integer.

02

Area 

The area of the curve is given by,

A=12鈭�伪尾r2d胃A=12鈭�02蟺a2d胃A=12a3302蟺A=2蟺36-0A=8蟺36A=4蟺36unit2

The area of the curve isA=4蟺36unit2

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Most popular questions from this chapter

In Exercises 32鈥�47 convert the equations given in polar coordinates to rectangular coordinates.
r=6csc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

r=e胃for2k蟺鈮�胃鈮�2(k+1)蟺

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

Thespiralr=e伪胃for0鈮�胃鈮�2蟺

Measurements indicate that Earth鈥檚 orbital eccentricity is 0.0167and its semimajor axis is 1.00000011astronomical units.

(a) Write a Cartesian equation for Earth鈥檚 orbit.

(b) Give a polar coordinate equation for Earth鈥檚 orbit, assuming that the sun is the focus of the elliptical orbit.

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

r=21+cos胃
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