Question Detail

MTH 102 MTH 102 Past Questions Objective Question
Take CBT

Question

Evaluate ∫ dx / (x² + 4x + 7)
Options
A (1/&radic;2) tan<sup>-1</sup>((x+3)/&radic;2) + C
B (1/&radic;3) tan<sup>-1</sup>((x+2)/&radic;3) + C
Correct Answer
C (1/&radic;6) tan<sup>-1</sup>((x+7)/&radic;6) + C
D (1/&radic;5) tan<sup>-1</sup>((x+6)/&radic;5) + C
Correct Answer

Option B is the correct answer.

Detailed Explanation

To evaluate this integral, we first complete the square in the denominator:x² + 4x + 7 = (x² + 4x + 4) + 3 = (x+2)² + (√3)².Now the integral is in the form ∫ du / (u² + a²), where u = x+2 and a = √3.The standard integral formula for this form is (1/a) tan-1(u/a) + C.Substitute u = x+2 and a = √3:(1/√3) tan-1((x+2)/√3) + C.This matches option B.

Hint

Complete the square in the denominator to transform the integral into a standard arctangent form (∫ du / (u² + a²)).

Question Info

Course: MTH 102
Topic: MTH 102 Past Questions
Type: Objective
Difficulty: Not specified
Question 586 of 930
Previous Course Details Next