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MTH 102 MTH 102 Past Questions Objective Question
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Question

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

Option A is the correct answer.

Detailed Explanation

This integral can be simplified using a u-substitution.Let u = x3.Now, find the differential du by differentiating u with respect to x:du/dx = d/dx(x3) = 3x2So, du = 3x2 dx.Substitute u and du into the integral:∫ eu duNow, integrate with respect to u:= eu + CFinally, substitute u = x3 back into the expression:= ex3 + CThis matches option A.

Hint

Look for a part of the integrand whose derivative is also present in the integrand. Here, the derivative of x3 is 3x2.

Question Info

Course: MTH 102
Topic: MTH 102 Past Questions
Type: Objective
Difficulty: Not specified
Question 745 of 930
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