Calculate the double integral R x/1+xydA, R=[0,1]x [0,1]

DofotheroU

DofotheroU

Answered question

2021-10-02

Calculate the double integral R x/1+xydA, R=[0,1]x [0,1]

Answer & Explanation

Faiza Fuller

Faiza Fuller

Skilled2021-10-03Added 108 answers

We are integrating over the unit square in the plane. Use the fact that the numerator is the derivative of the denominator when taken with respect to y. This enables us to instantly solve the integral with respect to y since :
f(y)f(y)dy=ln|f(y)|+C
By using the formula above we compute:
0101x1+xydydx=01ln(1+x)ln1dx=
Now use the integration by parts:
01ln(1+x)dx=2ln21
Result:
2ln21

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