Question
Consider the following for the two (02) items that follow: Let the function y = (1 - x)^ -1 , where x 2n and n is an integer. What is y \, dx equal to?
NDA
Mathematics
Indefinite Integration
2025
NDA 2025 (Phase 1)
NDA Mathematics Question (2025) — Solution
Options
- A. - (x/2) + c
- B. - (x/2) + c
- C. (x/2) + c
- D. (x/2) + c
Answer
B. - (x/2) + c
Step-by-step solution
Given y = (1 - x)^ -1 y = 1 1 - x Using the half-angle formula 1 - x = 2 ^2(x/2) y = 1 2 ^2(x/2) = 1 2 ^2(x/2) Integrating with respect to x: y \, dx = 1 2 ^2(x/2) \, dx y \, dx = 1 2 ( - (x/2) 1/2 ) + c y \, dx = - (x/2) + c Answer: - (x/2) + c
Related: Mathematics — Indefinite Integration · All PYQ Banks