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MTH 102 MTH 102 Past Questions Objective Question
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Question

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

Option B is the correct answer.

Detailed Explanation

This integral can be solved using u-substitution.Let u = x3.Then, calculate the differential du:du/dx = 3x2du = 3x2 dx.Substitute u and du into the integral:∫ eu du.The integral of eu is eu.So, ∫ eu du = eu + C.Substitute back u = x3:= ex3 + C. This matches option B.

Hint

Look for a composite function where the derivative of the inner function is also present (or a constant multiple thereof) in the integrand. This suggests u-substitution. Let u be the inner function x3.

Question Info

Course: MTH 102
Topic: MTH 102 Past Questions
Type: Objective
Difficulty: Not specified
Question 784 of 930
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