Use symmetry to evaluate the double integral. \int\int_{R}\frac{4xy}{1+x^{2}}dA, R=\{(x,y)|-4\leq x \leq

Phoebe

Phoebe

Answered question

2021-10-23

Use symmetry to evaluate the double integral.
R4xy1+x2dA,R={(x,y)4x4,0y1}

Answer & Explanation

faldduE

faldduE

Skilled2021-10-24Added 109 answers

Step 1
When the upper and lower limits of definite integrals become same, the result is zero irrespective of the function to be integrated.
Definite integrals are generally used in calculating area, volume of curves defined under a certain interval.
Step 2
=44014xy1+x2dxdy
=444x1+x2dx01ydy
=444x1+x2dx(12)
=442x1+x2dx
Let 1+x2=t
then 2xdx=dt
=17171tdt
=0

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