n = 1 ∑ ∞ ∬ R ( x 2 + y 2 y ) n d x d y
Given that R = { ( x , y ) ∈ R 2 : y ≤ x , x 2 + y 2 ≤ 2 , y ≥ 0 } .
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Thank you Sir. Have a wonderfull day.
Sir I can you give complete solution.I dont know how to use polar co-ordinate in double integral
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Nice problem! I will have to assign it in one of my classes some time...
In polar coordinates, the double integral is ∫ 0 π / 4 ∫ 0 2 sin n ( θ ) r d r d θ = ∫ 0 π / 4 sin n ( θ ) d θ . Summing the geometric series of sine powers, we find ∫ 0 π / 4 1 − sin ( θ ) sin ( θ ) d θ ≈ 0 . 6 2 8