Question Detail

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

We can solve this integral using a substitution.Let u = x3.Then, the differential du = d/dx(x3) dx = 3x2 dx.Substitute these into the integral:∫ eu duThe integral of eu with respect to u is eu + C.Now, substitute back u = x3:ex3 + C.

Hint

Look for a substitution where the derivative of the substituted term is present in the integrand.

Question Info

Course: MTH 102
Topic: MTH 102 Past Questions
Type: Objective
Difficulty: Not specified
Question 686 of 930
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