Question
If I_1 = _e^ e^2 dx x and I_2 = _1^2 e^x x \, dx, then which one of the following is correct?
NDA
Mathematics
Definite Integration
2025
NDA 2025 (Phase 2)
NDA Mathematics Question (2025) — Solution
Options
- A. I_1 - I_2 = 0
- B. I_1 + I_2 = 0
- C. I_1 - 2I_2 = 0
- D. 2I_1 - I_2 = 0
Answer
A. I_1 - I_2 = 0
Step-by-step solution
I_1 = _e^ e^2 dx x Substituting x = t x = e^t dx = e^t dt When x = e, t = 1 When x = e^2, t = 2 I_1 = _1^2 e^t t dt Since the definite integral is independent of the variable of integration, I_1 = _1^2 e^x x dx = I_2 I_1 - I_2 = 0 Answer: I_1 - I_2 = 0
Related: Mathematics — Definite Integration · All PYQ Banks