Question Detail

MTH 102 MTH 102 Past Questions Objective Question
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Question

Find ∫ (cos x / sin2 x - 2e2x) dx
Options
A cosecx - e^(2x) + c
B -cosecx - 3e^(2x) + c
C -cosecx - e^(2x) + c
Correct Answer
D cosecx - 2e^(2x) + c
Correct Answer

Option C is the correct answer.

Detailed Explanation

We can integrate each term separately:∫ (cos x / sin2 x - 2e2x) dx = ∫ (cos x / sin2 x) dx - ∫ 2e2x dx.For the first term, cos x / sin2 x = (1/sin x) * (cos x / sin x) = cosec x cot x.The integral of cosec x cot x is -cosec x.For the second term, ∫ 2e2x dx. Let u = 2x, so du = 2 dx. The integral becomes ∫ eu du = eu = e2x.Combining these results, the indefinite integral is -cosec x - e2x + c.Therefore, option C is the correct answer.

Hint

Rewrite cos x / sin2 x using trigonometric identities (cosec x cot x), and use a simple substitution for the exponential term.

Question Info

Course: MTH 102
Topic: MTH 102 Past Questions
Type: Objective
Difficulty: Not specified
Question 305 of 930
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