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Chapter 13: Q. 28 (page 1015)

Let f(x, y) be a continuous function. Sketch each region 惟described in Exercises 25鈥�28. Then set up one or more (if necessary) iterated integrals to compute 鈭�惟f(x,y)dA,

(a) where you integrate first with respect to y and

(b) where you integrate first with respect to x.

惟=x,y|x2+y2鈮�9

Short Answer

Expert verified

The sketch of the region:

a) Integral is 鈭�-33鈭�-9-x29-x2f(x,y)dydx

b) Integral is鈭�-33鈭�-9-y29-y2f(x,y)dxdy

Step by step solution

01

Step 1. Given information

Given region:

惟=x,y|x2+y2鈮�9

02

Step 2. Sketch the region 

The region represents a circle of radius 3

03

part a) Set up integral with respect to y first.

x2+y2=9y2=9-x2y=9-x2

As we can see in the above sketch

When 3 then -9-x2鈮�y鈮�9-x2

So integral is set up as:

鈭�-33鈭�-9-x29-x2f(x,y)dydx

04

Part(b) Step 1.  Set up integral with respect to x first. 

x2+y2=9x2=9-y2x=9-y2

In the above sketch

When -3鈮�y鈮�3then -9-y2鈮�x鈮�9-y2

So integral is setup as

鈭�-33鈭�-9-y29-y2f(x,y)dxdy

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Most popular questions from this chapter

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