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

Rex+ydA,

whereR=x,y|0x1and0y1.

Short Answer

Expert verified

The value of double integral is :-

Rex+ydA=e-12

where,R=x,y|0x1and0y1

Step by step solution

01

Step 1. Given Information 

We have given the following double integral :-

Rex+ydA,

where R=x,y|0x1and0y1.

We have to evaluate this double integral.

02

Step 2. Use iterated integrals

The given double integral is :-

Rex+ydA,

where R=x,y|0x1and0y1.

Then by using Fubini's Theorem, we can writ this double integral as following :-

role="math" localid="1650413616232" Rex+ydA=0101ex+ydxdy

We can write this as following :-

0101ex+ydxdy=0101exeydxdy

Then by using iterated integrals, we have :-

role="math" localid="1650413690814" 0101exeydxdy=0101exeydxdy

Now we can solve this integral as following :-

0101exeydxdy=01eyex10dy=01eye1-e0dy=01eye-1dy=e-1ey10=e-1e1-e0=e-1e-1=e-12

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