Question Detail

MTH 102 MTH 102 Past Questions Objective Question
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Question

Integrate ∫ sin² x dx.
Options
A -cos² x
B 1 + cos² x
C x/2 - (sin x cos x)/2
Correct Answer
D x/2 - (sin 2x)/2
Correct Answer

Option C is the correct answer.

Detailed Explanation

To integrate sin² x, use the power-reducing identity: sin² x = (1 - cos(2x)) / 2.∫ sin² x dx = ∫ (1 - cos(2x)) / 2 dx= (1/2) ∫ (1 - cos(2x)) dx= (1/2) [x - (sin(2x))/2] + C= x/2 - (sin(2x))/4 + C.We know that sin(2x) = 2 sin x cos x.So, x/2 - (2 sin x cos x)/4 + C = x/2 - (sin x cos x)/2 + C.This matches option C.

Hint

Use the power-reducing identity for sin² x: sin² x = (1 - cos(2x))/2. Also recall the double angle formula for sine.

Question Info

Course: MTH 102
Topic: MTH 102 Past Questions
Type: Objective
Difficulty: Not specified
Question 447 of 930
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