Mathematics

$$\displaystyle\int_{0}^{\dfrac{\pi }{2}}\frac{\sqrt{\sin x}}{\sqrt{\sin x}+\sqrt{\cos x}}dx$$       


SOLUTION
$$I=\int_{0}^{\frac{\pi }{2}}\frac{\sqrt{sin x}}{\sqrt{sin x}+\sqrt{cos x}}dx$$ ------(1)
$$I=\int_{0}^{\frac{\pi }{2}}\frac{\sqrt{cos x}}{\sqrt{sin x}+\sqrt{cos x}}dx$$ ------ (2)
adding (1) & (2)
$$2I=\int_{0}^{\frac{\pi }{2}}\frac{\sqrt{sin x}+\sqrt{cos x}}{\sqrt{sin x}+\sqrt{cos x}}dx$$
$$2I=\int_{0}^{\frac{\pi }{2}}1.dx$$
$$2I=[x]_{0}^{\frac{\pi }{2}}=\frac{\pi }{2}$$
$$[I=\frac{\pi }{4}]$$
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Subjective Medium Published on 17th 09, 2020
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