Question Detail

MTH 102 MTH 102 Past Questions Objective Question
Take CBT

Question

Obtain the integral ∫sin(2x)/sin(x) dx.
Options
A cos²(2x)/2
B ln(cos(2x))
C 2sin(x)
Correct Answer
D sin(2x)
Correct Answer

Option C is the correct answer.

Detailed Explanation

First, use the double angle identity for sin(2x): sin(2x) = 2sin(x)cos(x).Substitute this into the integral:∫(2sin(x)cos(x))/sin(x) dxCancel out sin(x) (assuming sin(x) ≠ 0):∫2cos(x) dxThe integral of cos(x) is sin(x).= 2sin(x) + C.

Hint

Start by simplifying the integrand using a trigonometric identity. The double-angle identity for sine is key.

Question Info

Course: MTH 102
Topic: MTH 102 Past Questions
Type: Objective
Difficulty: Not specified
Question 460 of 930
Previous Course Details Next