Question Detail

MTH 102 MTH 102 Past Questions Objective Question
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Question

Find the integral: ∫ (cos x / sin² x - 2e^(2x)) dx
Options
A cosec x - e^(2x) + c
B -cosec x - 3e^(2x) + c
C -cosec x - e^(2x) + c
Correct Answer
D cosec x - 2e^(2x) + c
Correct Answer

Option C is the correct answer.

Detailed Explanation

We can split the integral into two parts: ∫ (cos x / sin² x) dx - ∫ (2e^(2x)) dx.For the first part, cos x / sin² x = (cos x / sin x) * (1 / sin x) = cot x cosec x.The integral of cot x cosec x dx is -cosec x.For the second part, the integral of 2e^(2x) dx is 2 * (1/2)e^(2x) = e^(2x).Combining these, the result is -cosec x - e^(2x) + C.

Hint

Rewrite the trigonometric term using identities and integrate the exponential term carefully.

Question Info

Course: MTH 102
Topic: MTH 102 Past Questions
Type: Objective
Difficulty: Not specified
Question 319 of 930
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