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Question Number 132261 by muneer0o0 last updated on 12/Feb/21

Answered by Olaf last updated on 13/Feb/21

$$\mathrm{\Omega }={\int }_{-1}^{+1}{\int }_{-\sqrt{1-y^2}}^{+\sqrt{1-y^2}}\sec (x^2+y^2)dxdy$$$$\mathrm{\Omega }={\int }_0^1{\int }_0^{2\pi }\sec \left(r^2\right)rd\theta dr$$$$\mathrm{\Omega }={\int }_0^1\frac{2\pi r}{\cos r^2}dr$$$$\mathrm{\Omega }=2\pi [\frac{1}{2}\ln (1+\sin \left(1\right))-\frac{1}{2}\ln \left(\cos \left(1\right)\right)]$$$$\mathrm{\Omega }=\pi \ln \left(\frac{1+\sin \left(1\right)}{\cos \left(1\right)}\right)$$

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