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  4. The value of I = ∫ limitsπ/ 20 ((sin x + cos x)2/√1+sin 2x)dx is

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Q. The value of $I = \int\limits^{\pi/ 2}_{0} \frac{\left(sin\, x + cos \,x\right)^{2}}{\sqrt{1+sin\,2x}}dx$ is

AIEEEAIEEE 2004Integrals

Solution:

$ \int\limits^{\frac{\pi}{2}}_{0} \frac{\left(sin\, x + cos \,x\right)^{2}}{\sqrt{\left(sin\, x + cos \,x\right)^{2}}}dx = \int\limits^{\frac{\pi}{2}}_{0}\left(sin\, x + cos \,x\right)dx = \left|sin\, x + cos \,x\right|^{\frac{\pi}{2}}_{0} = 2.$