Question

The value of int₀^π/2frac√(sin x)√(sin x)+√(cos x)dx is

• A. (π)/(2)
• B. -(π)/(2)
• C. (π)/(4)
• D. None of these

Hint:

Use symmetry: replace x by (π)/(2)-x.

Answer 1

The Correct Option is C

Let I=int₀^π/2frac√(sin x)√(sin x)+√(cos x)dx By symmetry, I=int₀^π/2frac√(cos x)√(sin x)+√(cos x)dx Adding, 2I=int₀^π/21dx=(π)/(2) ⟹ I=(π)/(4)