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Chapter 13: Q. 10 (page 1082)

Evaluating iterated integrals: Sketch the region determined by the limits of the given iterated integrals, and then evaluate the integrals.

鈭�02鈭�0yxy2-x2dxdy

Short Answer

Expert verified

鈭�02鈭�0yxy2-x2dxdy=12821

Step by step solution

01

Draw the region

The region determined by the limits of the given iterated integral is shown below,

02

Evaluate the given integral

I=鈭�0yxy2-x2dxSubstitute,y2-x2=u2Differentiatew.r.t.x-2xdx=2ududx=-uxdu

I=-鈭�0yxu2uxduI=-鈭�0yu2duI=-u33I=-y2-x2330yI=y63

Therefore,

鈭�02鈭�0yxy2-x2dxdy=13鈭�02y6dy=13y7702=12821

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Most popular questions from this chapter

Evaluate each of the double integrals in Exercises37-54as iterated integrals.

localid="1650380493598" 鈭�鈭�Rsin2x+ydA,

wherelocalid="1650380496793" R=x,y|0鈮�x鈮�蟺2and0鈮�y鈮�蟺2

Evaluate the triple integrals over the specified rectangular solid region.

鈭�R鈥�x2yzdV, whereR={(x,y,z)鈭�鈭�2鈮�x鈮�1,0鈮�y鈮�3,and1鈮�z鈮�5}

Evaluate each of the double integrals in Exercises 37鈥�54 as iterated integrals.

鈭�鈭�Rx2cos(xy)dA,whereR={(x,y)|0鈮�x鈮�蟺and0鈮�y鈮�1}

Evaluate the iterated integral :

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

In Exercises 45鈥�52, rewrite the indicated integral with the specified order of integration.

Exercise 42 with the order dy dx dz.
See all solutions

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