Question Detail

MTH 102 MTH 102 Past Questions Objective Question
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Question

Simplify ∫ 3x2ex3 dx
Options
A e<sup>x<sup>2</sup></sup> + C
B e<sup>x<sup>3</sup></sup> + C
Correct Answer
C e<sup>x<sup>4</sup></sup> + C
D e<sup>x<sup>5</sup></sup> + C
Correct Answer

Option B is the correct answer.

Detailed Explanation

This integral can be solved using u-substitution. Let u = x3. Then, find the differential du:du = d/dx(x3) dx = 3x2 dx.Substitute u and du into the integral: ∫ eu du.The integral of eu with respect to u is eu + C.Substitute back u = x3 to get the final answer: ex3 + C.

Hint

Look for a function and its derivative within the integral. Consider a substitution where u = x3.

Question Info

Course: MTH 102
Topic: MTH 102 Past Questions
Type: Objective
Difficulty: Not specified
Question 639 of 930
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