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

$$calculate\int \int {}_{D}cos(x^2+y^2)dxdywithD=C(o.\sqrt{\frac{\pi }{2}}).$$

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

Answered by ajfour last updated on 25/Dec/17

$$={\int }_0^{2\pi }{\int }_0^{\sqrt{\frac{\pi }{2}}}\left(\cos r^2\right)\left(rdr\right)d\theta$$$$if{r}^2=x^2+y^2$$$$=\pi {\int }_0^{\sqrt{\pi /2}}\left(\cos r^2\right)\left(2rdr\right)$$$$=\pi \left(\sin r^2\right){\mid }_0^{\sqrt{\pi /2}}=\mathit{\pi }.$$

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