Question Detail
Question
Obtain ∫sin²x dx
Correct Answer
Option D is the correct answer.
Detailed Explanation
To integrate sin²x, use the half-angle identity: sin²x = (1 - cos(2x))/2.Now, integrate the expression:∫sin²x dx = ∫(1 - cos(2x))/2 dx= 1/2 ∫(1 - cos(2x)) dx= 1/2 [x - (sin(2x)/2)] + C= 1/2 x - sin(2x)/4 + C.This matches option D.
Hint
Use a trigonometric identity to convert sin²x into an expression that is easier to integrate. The half-angle identity for sin²x is useful here.