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MTH 102 MTH 102 Past Questions Objective Question
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Question

Which of the following is true about In = ∫tann x dx, In =
Options
A (tan<sup>n-1</sup> x)/(n-1) - I<sub>n-2</sub>
Correct Answer
B tan<sup>n</sup> x / (n-1) + I<sub>n-2</sub>
C tan<sup>n</sup> x / n - I<sub>n-2</sub>
D tan<sup>n+1</sup> x / (n+1) - I<sub>n-2</sub>
Correct Answer

Option A is the correct answer.

Detailed Explanation

This is a standard reduction formula for ∫tann x dx.We can rewrite tann x as tann-2 x ⋅ tan² x.∫tann x dx = ∫tann-2 x (sec² x - 1) dx= ∫tann-2 x sec² x dx - ∫tann-2 x dxFor the first integral, let u = tan x, so du = sec² x dx.∫un-2 du = un-1 / (n-1) = tann-1 x / (n-1).The second integral is In-2.So, In = tann-1 x / (n-1) - In-2.This matches option A.

Hint

Rewrite tann x using the identity tan²x = sec²x - 1 and then use u-substitution for the first part of the integral.

Question Info

Course: MTH 102
Topic: MTH 102 Past Questions
Type: Objective
Difficulty: Not specified
Question 348 of 930
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