Calculate the double integral =\int \int_{R} \frac{4x}{1+xy}dA, R=[0, 4] \times [0,

akutagawatj

akutagawatj

Answered question

2021-11-26

Calculate the double integral
=R4x1+xydA,R=[0,4]×[0,1]

Answer & Explanation

Royce Moore

Royce Moore

Beginner2021-11-27Added 17 answers

Step 1
The given integrals is =R4x1+xydA wrehe
=R=0,4×[0,1]
Evaluate as follows
Step 2
=R4x1+xydA=01044x1+xydxdy
=40104(1y1y(1+xy))dxdy
=401[xyln(1+xy)y2]04dy
=401(4yln(1+xy)x2)dy
=4014y2(4y{ln(1+4y)}4)
=4[5In(5)4] (by uv meth
=4(5In(5)4)
Thus, =R4x1+xy(5In(5)4).

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