Question Detail

MTH 102 MTH 102 Past Questions Objective Question
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Question

Obtain ∫ xe^(x²) dx.
Options
A (1/2)e^(x²) + C
Correct Answer
B -(1/2)e^(x²) + C
C (1/2)e^(-x²) + C
D -(1/2)e^(-x²) + C
Correct Answer

Option A is the correct answer.

Detailed Explanation

To solve ∫ xe^(x²) dx, use u-substitution. Let u = x². Differentiate u with respect to x: du/dx = 2x, so du = 2x dx. This means x dx = (1/2) du. Substitute these into the integral: ∫ e^u (1/2) du = (1/2) ∫ e^u du. The integral of e^u is e^u. So, (1/2)e^u + C. Substituting back u = x², the final answer is (1/2)e^(x²) + C.

Hint

Use u-substitution. Let u be the exponent of e. Notice that the derivative of the exponent is present as a factor in the integrand.

Question Info

Course: MTH 102
Topic: MTH 102 Past Questions
Type: Objective
Difficulty: Not specified
Question 368 of 930
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