Question Detail

MTH 102 MTH 102 Past Questions Objective Question
Take CBT

Question

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

Option C is the correct answer.

Detailed Explanation

To obtain ∫ xe^(-x²) dx, we use the substitution method:
  1. Let u = -x².
  2. Differentiate u with respect to x:du/dx = -2xThis implies du = -2x dx.
  3. Rearrange to find x dx:x dx = -1/2 du.
  4. Substitute u and x dx into the integral:∫ e^u (-1/2) du
  5. Integrate with respect to u:-1/2 ∫ e^u du = -1/2 e^u + C
  6. Substitute back u = -x²:-1/2 e^(-x²) + C
This matches option C.

Hint

Consider using a u-substitution. Look for a part of the integrand whose derivative is also present (or a constant multiple of it).

Question Info

Course: MTH 102
Topic: MTH 102 Past Questions
Type: Objective
Difficulty: Not specified
Question 433 of 930
Previous Course Details Next