calculate-D-cos-x-2-y-2-dxdy-with-D-C-o-pi-2-

Question Number 26399 by abdo imad last updated on 25/Dec/17

c a l c u l a t e \int \int_{D} c o s (x^{2} + y^{2}) d x d y w i t h D = C (o . \sqrt{\frac{π}{2}}) .

Answered by kaivan.ahmadi last updated on 25/Dec/17

Answered by ajfour last updated on 25/Dec/17

= \int_{0}^{2 π} \int_{0}^{\sqrt{\frac{π}{2}}} (\cos r^{2}) (r d r) d θ

i f r^{2} = x^{2} + y^{2}

= π \int_{0}^{\sqrt{π / 2}} (\cos r^{2}) (2 r d r)

= π (\sin r^{2}) ∣_{0}^{\sqrt{π / 2}} = π .

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