Evaluate the following definite integral: `int_0^(pi//2)sqrt(1+cosx\ )dx`

Explanation

`\int_{0}^{\pi / 2} \sqrt{1+\cos x} d x=\int_{0}^{\pi / 2}(\sqrt{1+\cos x}) \times \frac{\sqrt{1-\cos x}}{\sqrt{1-\cos x}} d x`


.`\Rightarrow \int_{0}^{\frac{\pi}{2}}(\sqrt{1+\cos x}) d x=\int_{0}^{\frac{\pi}{2}}[\frac{(\sqrt{1-\cos ^{2} x})}{\sqrt{1-\cos x}})] d x`



`\Rightarrow \int_{0}^{\frac{\pi}{2}}(\sqrt{1+\cos x}) d x=\int_{0}^{\frac{\pi}{2}}[\frac{\sqrt{\sin ^{2} x}}{\sqrt{1-\cos x}}] d x`



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