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Chapter 13: Q.33 (page 1004)

Evaluate Each of the integrals in exercises 33-36 as an iterated integral and then compare your answer with thoise you found in exercise 29-32

鈭�鈭�RxydAWhereR={(x,y)|0鈮�x鈮�2,1鈮�y鈮�4}

Short Answer

Expert verified

The value of integral is鈭�鈭�RxydAWhereR={(x,y)|0鈮�x鈮�2,1鈮�y鈮�4}is 15units

Step by step solution

01

Given information

We have given an integral鈭�鈭�RxydAWhereR={(x,y)|0鈮�x鈮�2,1鈮�y鈮�4}

02

Using iterated integral

Using the definition of iterated integrals we get,

鈭�14鈭�02xydxdy=鈭�14[x2y2]20dy=鈭�142ydy=[y2]41 =16-1=15

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Most popular questions from this chapter

Evaluate the iterated integral :

鈭�01鈥�鈭�03鈥�鈭�0sin鈭�1鈦�x鈥�(x+y)dzdydx

Expressthesum3e4+3e9+3e16+4e4+4e9+4e16usingdouble-summationnotation.

Evaluate the sums in Exercises 23鈥�28.

鈭�j=13鈭�k=12kj

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

Explain how to construct a Riemann sum for a function of two variables over a rectangular region.
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