Question Detail

MTH 102 MTH 102 Past Questions Objective Question
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Question

Evaluate ∫ cos3x dx
Options
A sin x - (1/3)sin<sup>3</sup>x + C
Correct Answer
B cos x + (1/3)cos<sup>3</sup>x + C
C sec x - (1/3)sec<sup>3</sup>x + C
D tan x - (1/3)tan<sup>3</sup>x + C
Correct Answer

Option A is the correct answer.

Detailed Explanation

To integrate cos3x, we can rewrite it using the identity cos2x = 1 - sin2x.∫ cos3x dx = ∫ cos2x * cos x dx= ∫ (1 - sin2x) * cos x dxNow, use 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) + CFinally, substitute back u = sin x:= sin x - (sin3x)/3 + CThis matches option A.

Hint

Rewrite cos3x as cos2x * cos x and use the identity cos2x = 1 - sin2x before applying substitution.

Question Info

Course: MTH 102
Topic: MTH 102 Past Questions
Type: Objective
Difficulty: Not specified
Question 771 of 930
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