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Chapter 13: Q. 41 (page 1004)

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}

Short Answer

Expert verified

The value of the integral is 0

Step by step solution

01

Given information

We are given that鈭�鈭�Rsin(x+2y)dAWhereR={(x,y)|0鈮�x鈮�蟺,0鈮�y鈮�蟺2}

02

Use iterated integral

We have,

鈭�0蟺2鈭�0蟺sin(x+2y)dxdy=鈭�0蟺2鈭�0蟺(sinxcos2y+sin2ycosx)dxdy=鈭�0蟺2[-cosxcos2y+sin2ysinx]蟺0dy=鈭�0蟺2(cos2y)dy=[sin2y2]蟺20=0

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Most popular questions from this chapter

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

鈭�RxydA

where

R={(x,y)鈭�0鈮�x鈮�2&1鈮�y鈮�4}

Evaluate each of the integrals in exercise 33-36 as iterated integrals and then compare your answers with those you found in exercise 29-32

鈭�鈭�Rx2y3dAWhereR={(x,y)|1鈮�x鈮�3,0鈮�y鈮�2}

Find the volume between the graph of the given function and the xy-plane over the specified rectangle in the xy-plane

f(x,y)=-2x2y3WhereR={(x,y)|-2鈮�x鈮�3,-1鈮�y鈮�5}

Explain why it would be difficult to evaluate the double integrals in Exercises 18 and 19 as iterated integrals.

鈭�鈭�RcosxydAwhereR=x,yI蟺4鈮�x鈮�蟺2and蟺2鈮�y鈮�蟺

Explain how the Fundamental Theorem of Calculus is used in evaluating the iterated integral 鈭�ab鈭�cdf(x,y)dydx.
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