Question Detail
Question
Obtain ∫sin² x dx
Correct Answer
Option D is the correct answer.
Detailed Explanation
To integrate sin² x, we use the power-reduction trigonometric identity:sin² x = (1 - cos 2x)/2Now, substitute this into the integral:∫sin² x dx = ∫(1 - cos 2x)/2 dx= 1/2 ∫(1 - cos 2x) dxIntegrate term by term:= 1/2 (∫1 dx - ∫cos 2x dx)= 1/2 (x - sin 2x/2) + CDistribute the 1/2:= 1/2x - sin 2x/4 + C. This matches option D.
Hint
Use the trigonometric identity sin² x = (1 - cos 2x)/2 to simplify the integrand before integration.