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Chapter 9: Q. 7 (page 774)

Fill in the blanks to complete each of the following theorem statements:

Let 伪and 尾 be real numbers such that 0鈮�尾-伪鈮�2蟺.Let R be the region in the polar plane bounded by the rays 胃=伪and 胃=尾and a positive continuous functionr=f(胃). Then the area of region R is ................

Short Answer

Expert verified

The blank is filled by12鈭�伪尾f胃2d胃.

Step by step solution

01

Step 1. Given information

R is the region in the polar plane bounded by the rays 胃=伪and 胃=尾 and a positive continuous functionr=f(胃).

02

Step 2. Area of the region.

Since the area of a sector of an circle having radius rand center angle 蠒rad is:

A=12蠒r2

The area of the region will be the limit of the Riemann sum as n鈫�鈭�.

role="math" localid="1653108596825" limn鈫�鈭�鈭�121nf胃k2鈭�胃

So,

The area of the region is;

A=12鈭�伪尾r2d胃=12鈭�伪尾f(胃)2d胃

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Most popular questions from this chapter

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

foci(卤5,1), major axis6

Complete example 2 by evaluating the integral expression

鈭�02蟺3(12+cos胃)2d胃-鈭�蟺4蟺3(12+cos胃)2d胃

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

r2=cos胃

Given two points in a plane, called _______, a hyperbola is the set of points in the plane for which ________.

In Exercises 32鈥�47 convert the equations given in polar coordinates to rectangular coordinates.
胃=-蟺6
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