Question Detail
Question
Evaluate ∫ cos3x dx
Correct Answer
Option A is the correct answer.
Detailed Explanation
To evaluate ∫ cos3x dx, we use the trigonometric identity cos2x = 1 - sin2x.∫ cos3x dx = ∫ cos2x ∙ cos x dx= ∫ (1 - sin2x) ∙ cos x dx.Now, use u-substitution. Let u = sin x.Then, du = cos x dx.Substitute u and du into the integral:= ∫ (1 - u2) du.Integrate term by term:= u - (u3/3) + C.Substitute back u = sin x:= sin x - (sin3x)/3 + C. This matches option A.
Hint
Rewrite cos3x as cos2x ∙ cos x and then use the identity cos2x = 1 - sin2x. After that, use u-substitution with u = sin x.