Question Detail

MTH 102 MTH 102 Past Questions Objective Question
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Question

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

Option B is the correct answer.

Detailed Explanation

To evaluate this integral, complete the square in the denominator.x2 + 4x + 7 = (x2 + 4x + 4) + 3 = (x+2)2 + (√3)2.The integral is now of the form ∫ du / (u2 + a2), where u = x+2 and a = √3.The formula for this integral 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.

Question Info

Course: MTH 102
Topic: MTH 102 Past Questions
Type: Objective
Difficulty: Not specified
Question 801 of 930
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