Question Detail
Question
Obtain ∫sin²xdx.
Correct Answer
Option C is the correct answer.
Detailed Explanation
Use the power-reducing identity for sine: sin²x = (1 - cos 2x) / 2.∫ sin²x dx = ∫ (1 - cos 2x) / 2 dx= (1/2) ∫ (1 - cos 2x) dx= (1/2) [x - (sin 2x)/2] + C= x/2 - (sin 2x)/4 + C.Now, use the double angle identity sin 2x = 2 sin x cos x.So, (sin 2x)/4 = (2 sin x cos x)/4 = (sin x cos x)/2.Substitute this back: x/2 - (sin x cos x)/2 = (x - sin x cos x)/2.This matches option C.
Hint
Use the power-reducing identity sin²x = (1 - cos 2x) / 2 to simplify the integrand before integration. Then, remember the double angle identity sin 2x = 2 sin x cos x.