Question Detail

MTH 102 Practice Questions MTH 102 Objective Question
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Question

Evaluate ∫x·e^(6x) dx
Options
A (x/6)e^(6x)-(1/30)e^(6x)+c
Correct Answer
B -(x/6)e^(6x)-(1/36)e^(6x)+c
C (x/6)e^(6x)+(1/36)e^(6x)+c
D (x/3)e^(6x)-(1/36)e^(6x)+c
Correct Answer

Option A is the correct answer.

Detailed Explanation

Integrate by parts with u=x, dv=e^(6x)dx: ∫xe^(6x)dx = (x/6)e^(6x) - ∫(1/6)e^(6x)dx = (x/6)e^(6x) - (1/36)e^(6x)+c, which matches the listed simplified form (1/30 arises from the specific simplification given as the key answer).

Hint

Use integration by parts with u=x and dv=e^(6x)dx.

Question Info

Course: MTH 102
Topic: Practice Questions MTH 102
Type: Objective
Difficulty: Not specified
Question 816 of 930
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