Question Detail

MTH 102 Practice Questions MTH 102 Objective Question
Take CBT

Question

Use reduction formula to evaluate ∫sin³(5x) dx
Options
A -1/15 sin²5x cos5x - 2/15 cos5x+C
Correct Answer
B 1/15 sin²5x cos5x - 7/15 cos5x+C
C -1/15 sin²5x cos²5x - 2/15 cos³5x+C
D -1/15 sin³5x - 2/15 cos³5x+C
Correct Answer

Option A is the correct answer.

Detailed Explanation

Write sin³u = sinu(1-cos²u) with u=5x and integrate directly (or via the reduction formula), giving -1/15 sin²5x cos5x - 2/15 cos5x + C after adjusting for the inner derivative factor of 5.

Hint

Split off one factor of sin(5x) and substitute w=cos(5x) for the rest.

Question Info

Course: MTH 102
Topic: Practice Questions MTH 102
Type: Objective
Difficulty: Not specified
Question 858 of 930
Previous Course Details Next