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MTH 102 MTH 102 Past Questions Objective Question
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Question

Simplify ∫ 3x² e^(x³) dx
Options
A e^(x³) + C
Correct Answer
B e^(x⁴) + C
C e^(x³) + C
D e^(x⁵) + C
Correct Answer

Option A is the correct answer.

Detailed Explanation

To evaluate the integral ∫ 3x² e^(x³) dx, we use a substitution.Let u = x³. Then, the differential du = d/dx(x³) dx = 3x² dx.Substituting these into the integral, we get ∫ e^u du.The integral of e^u with respect to u is e^u + C.Finally, substitute back u = x³ to get the result: e^(x³) + C.

Hint

Look for a substitution where one part of the integrand is the derivative of another part. Consider u = x³.

Question Info

Course: MTH 102
Topic: MTH 102 Past Questions
Type: Objective
Difficulty: Not specified
Question 609 of 930
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