Question Detail
Question
Evaluate ∫ Cos3 x dx.
Correct Answer
Option A is the correct answer.
Detailed Explanation
To evaluate ∫ Cos3 x dx, we use trigonometric identities.Rewrite Cos3 x as Cos2 x * Cos x.∫ Cos2 x * Cos x dxUse the identity Cos2 x = 1 - Sin2 x:∫ (1 - Sin2 x) Cos x dxNow, use u-substitution. Let u = Sin x, then du = Cos x dx.Substitute u and du into the integral:∫ (1 - u2) duIntegrate term by term:= u - (u3/3) + CSubstitute back u = Sin x:= Sin x - (Sin3 x)/3 + C.This matches option A.
Hint
Use the trigonometric identity Cos2x = 1 - Sin2x, and then apply u-substitution.