Evaluate the following definite integral: ∫ √(1 + sin x)dx, x ∈ [0, π/2 ]

Question

Evaluate the following definite integral:

\(\int\limits_0^{{\pi/}2}(\sqrt{1+sin\,\text x})d\text x \) 

Answer 1

\(\int\limits_0^{{\pi/}2}(\sqrt{1+sin\,\text x})d\text x \)

Let 1 – sin x = t². Hence, – cos x dx = 2 t dt and cos x dx = – 2 t dt.