Question Detail

MTH 102 MTH 102 Past Questions Objective Question
Take CBT

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 duIntegrate with respect to u:= eu + CSubstitute back u = x3:= ex3 + C.This matches option B.

Hint

Look for a function and its derivative within the integrand. Try u-substitution with u = x3.

Question Info

Course: MTH 102
Topic: MTH 102 Past Questions
Type: Objective
Difficulty: Not specified
Question 658 of 930
Previous Course Details Next