Calculate the double integral. \int\int\frac{2(1+x^2)}{1+y^2}dA

e1s2kat26 2021-10-14 Answered
Calculate the double integral.
2(1+x2)1+y2dA,
where  R={(x,y)0x2,0y1}
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Expert Answer

2abehn
Answered 2021-10-15 Author has 88 answers

Step 1
It is given that R={(x,y)|0x2,0y1}.We have to find
R2(1+x2)1+y2dA
Notice that
R2(1+x2)1+y2dA={y=0}1{x=0}12(1+x2)1+y2dxdy
=01[21+y2021+x2dx]dy=01[21+y2(2+83)]dy
=01(283(1+y2))dy
=2830111+y2dy
=283[arctan(y)]01     [11+y2dy=arctan(y)]
y=283π4
=7π3
Result
01022(1+x2)1+y2dxdy=7π3

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