Question Detail

MTH 102 Practice Questions MTH 102 Objective Question
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Question

Determine the indefinite integral ∫cos⁴x dx
Options
A ¼cos³x sinx + 3/8 cosx sinx + 3x/8 + C
Correct Answer
B ¼cos³x sinx - 3/8 cosx sinx + 3x/8 + C
C ¼cos³x sinx + 3/8 cosx sinx + 5x/8 + C
D ¼cos³x sinx + 3/8 sin²x + 3x/8 + C
Correct Answer

Option A is the correct answer.

Detailed Explanation

Using the reduction formula for ∫cosⁿx dx repeatedly on cos⁴x gives ¼cos³x sinx + 3/8 cosx sinx + 3x/8 + C.

Hint

Apply the cosine reduction formula twice, stepping down from n=4 to n=2 to n=0.

Question Info

Course: MTH 102
Topic: Practice Questions MTH 102
Type: Objective
Difficulty: Not specified
Question 865 of 930
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