Calculate the double integral. \int\int_R\frac{1}{1+x+y}dA,\ R=[1,3]\time

Ramsey 2021-10-15 Answered
Calculate the double integral.
R11+x+ydA, R=[1,3]×[1,2]
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Expert Answer

broliY
Answered 2021-10-16 Author has 97 answers
Once again use the fact that:
f(x)f(x)dx=ln|f(x)|+C
It doesn't matter do you opt to solve the first integral with respect to x or with respect to y, Here, we opt to solve the integral with respect to y first:
131211+x+ydydx=13ln(x+3)ln(x+2)
Now using the integration by parts we obtain that the integral is equal to:
((x+3)ln(x+3)(x+3))((x+2)ln(x+2)(x+2))13=6ln65ln54ln4+3ln3
Result: 6ln65ln54ln4+3ln3
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