Question Detail
Question
Obtain ∫ sin²x dx
Correct Answer
Option D is the correct answer.
Detailed Explanation
To integrate sin²x, we use the power-reducing identity: 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.The mathematically correct answer is x/2 - (sin 2x)/4. The highlighted option D is x/2 + (sin 2x)/4, which has a sign error.
Hint
Use the power-reducing trigonometric identity for sin²x, which is sin²x = (1 - cos 2x) / 2.