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MTH 102 MTH 102 Past Questions Objective Question
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Question

Which of the following option best represents the reduction formula for ∫secⁿ x dx, n≥2?
Options
A (1/(n-1))secⁿ⁻¹x tan x + ((n-2)/(n-1))∫secⁿ⁻²x dx
B (1/(n-1))secⁿ⁻²x tan x - ((n-2)/(n-1))∫secⁿ⁻²x dx
C (1/(n-1))secⁿ⁻²x tan x + ((n-2)/(n-1))∫secⁿ⁻²x dx
Correct Answer
D (1/(n))secⁿ⁻¹x tan x + ((n-1)/(n))∫secⁿ⁻²x dx
Correct Answer

Option C is the correct answer.

Detailed Explanation

The reduction formula for the integral of powers of secant, ∫secⁿ x dx for n≥2, is a standard result derived using integration by parts. The formula is:∫secⁿ x dx = (1/(n-1))secⁿ⁻²x tan x + ((n-2)/(n-1))∫secⁿ⁻²x dx.Option C perfectly matches this standard reduction formula.

Hint

Recall the standard reduction formula for ∫secⁿ x dx. This formula is often derived using integration by parts with u = secⁿ⁻²x and dv = sec²x dx.

Question Info

Course: MTH 102
Topic: MTH 102 Past Questions
Type: Objective
Difficulty: Not specified
Question 393 of 930
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