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Chapter 13: Q 12. (page 1014)

Which of the iterated integrals in Exercises 9鈥�12 could correctly be used to evaluate the double integral 鈭�0f(x,y)dA

鈭�20鈭�-y+20f(x,y)dxdy

Short Answer

Expert verified

鈭�02鈭�0-y+2f(x,y)dxdywill give the correct value of the given integral.

Step by step solution

01

Given Information

Rectangular region is bounded below by xand on left by yaxis and along liney=-x+2

02

Consideration

Consider iterated integral

鈭�20鈭�-y+20f(x,y)dxdy

Region is triangular and can be of any type.

For type II region, inner integral is solved wrt x.

This is not true for iterated integral鈭�20鈭�-y+20f(x,y)dxdy

03

Simplification

Keeping the order of integral same, limits of both inner and outer integral should be reversed.

鈭�02鈭�0-y+2f(x,y)dxdy

Therefore, iterated integral 鈭�02鈭�0-y+2f(x,y)dxdywill give the 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�Rsin(x+2y)dAWhereR={(x,y)|0鈮�x鈮�蟺,0鈮�y鈮�蟺2}

Howmanysummandsarein鈭�j=313鈭�k=520j2ejk?

Use Definition 13.4to evaluate the double integrals in Exercises 29鈥�32.

localid="1649936867482" 鈭�xx2ydA

whereR={(x,y)鈭�1鈮�x鈮�3and0鈮�y鈮�2}

Describe the three-dimensional region expressed in each iterated integral in Exercises 35鈥�44.

鈭�-33鈭�-9-x29-x2鈭�-9-x2-y29-x2-y2f(x,y,z)dzdydx

Describe the three-dimensional region expressed in each iterated integral:

鈭�鈭�24鈥�鈭�26鈥�鈭�05鈥�f(x,y,z)dydxdz
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