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Chapter 13: Q 10. (page 1014)

Which of the iterated integrals in Exercises 9鈥�12 could correctly be used to evaluate the double integral 鈭�惟f(x,y)dA

鈭�0-x+2鈭�02f(x,y)dxdy

Short Answer

Expert verified

The iterated integral that will give correct value of integral is鈭�02鈭�0-x+2f(x,y)dydx

Step by step solution

01

Given Information

It is given that region is bounded on left byyaxis and on left byxaxis.

02

Consideration

Consider iterated integral

鈭�0-x+2鈭�02f(x,y)dxdy

Region is triangular and can be of any type.

The inner integral is solved wrt yfor type I.

03

Simplification

But in iterated integral 鈭�-x+2鈭�2f(x,y)dxdy, inner integral is wrt y

Hence, it will give incorrect value of 鈭�惟f(x,y)dA

The limits will be interchanged and hence the correct integral is鈭�02鈭�0-x+2f(x,y)dydx

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