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Question Number 192543 by peter frank last updated on 20/May/23

Answered by leodera last updated on 20/May/23

$$\mathrm{\Delta }={\int }_0^{\frac{\pi }{2}}\frac{\sin \left(x\right)}{\sin \left(x\right)+\cos \left(x\right)}dx$$$$\mathrm{\Delta }=\frac{1}{2}{\int }_0^{\frac{\pi }{2}}\frac{\sin \left(x\right)+\cos \left(x\right)}{\sin \left(x\right)+\cos \left(x\right)}dx=\frac{1}{2}{\int }_0^{\frac{\pi }{2}}dx$$$$\mathrm{\Delta }=\frac{\pi }{4}$$$$$$$$$$

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