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

RexydAwhereR=x,yI1x2and1y3

Short Answer

Expert verified

The given double integral is difficult to evaluate using iterated integrals.

Step by step solution

01

Step 1. Given Information.

The iterated integral is,

RexydAwhereR=x,yI1x2and1y3

02

Step 2. Explanation.

Evaluating the first integral with respect to yand treating xas constant.

RexydA=1213exydydx=1213exydydx=121xexyy=1y=3dx=121xe3x-1xexdx

Now the resultant function 1xe3x-1xexdoes not have a simple anti-derivative to evaluate the next step which is integrating with respect to variablex. The given double integral is difficult to evaluate using iterated integrals.

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