The value of ∫√(1 + sin x) dx, isसमाकल ∫√(1 + sin x) dx का मान है

Explanation

1 + sin x = sin²(x/2) + cos²(x/2) + 2 sin(x/2)cos(x/2) = (sin(x/2) + cos(x/2))². So the integral is ∫(sin(x/2) + cos(x/2)) dx = −2cos(x/2) + 2sin(x/2) = 2(sin(x/2) − cos(x/2)) + C.1 + sin x = sin²(x/2) + cos²(x/2) + 2 sin(x/2)cos(x/2) = (sin(x/2) + cos(x/2))²। अतः समाकल ∫(sin(x/2) + cos(x/2)) dx = −2cos(x/2) + 2sin(x/2) = 2(sin(x/2) − cos(x/2)) + C।