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Chapter 13: Q 9. (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�02鈭�0-x+2f(x,y)dydx

Short Answer

Expert verified

The iterated integral will give correct value of鈭�惟f(x,y)dA

Step by step solution

01

Given Information

Rectangular region is bounded below xaxis, left byyaxis along the liney=-x+2

02

Simplification

Consider an iterated integral 鈭�02鈭�0-x+2f(x,y)dydx

The region is triangular region, can be of any type.

For type I region, inner integral is wrt y

In 鈭�02鈭�0-x+2f(x,y)dydx, inner integral is wrt y

It will give correct value of鈭�惟f(x,y)dA

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Most popular questions from this chapter

Evaluate each of the double integral in the exercise 37-54 as iterated integrals

鈭�鈭�R(3-x+4y)dAwhereR={(x,y)|0鈮�x鈮�1,-1鈮�y鈮�3}

Identify the quantities determined by the integral expressions in Exercises 19鈥�24. If x, y, and z are all measured in centimeters and 蚁(x, y,z) is a density function in grams per cubic centimeter on the three-dimensional region , give the units of the expression.

鈭�惟鈥�x蚁(x,y,z)dV

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State Fubini's theorem.

Evaluate the iterated integral :

鈭�0蟺/2鈥�鈭�0cos鈦�y鈥�鈭�0sin鈦�y鈥�(2x+y)dzdxdy
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