Question
Let f(t)= ( 1- ( _ e t ) 1- ( _ e t ) ) d t, t>1. If f (e^ / 2 )=-e^ / 2 and f (e^ / 4 )= e^ / 4 , then equals
JEE Main
Mathematics
Indefinite Integration
2026
JEE Main 2026 (24 January Shift 1)
JEE Main Mathematics Question (2026) — Solution
Options
- A. 1+ 2
- B. -1- 2
- C. -1-2 2
- D. -1+ 2
Answer
B. -1- 2
Step-by-step solution
Substituting u = t with dt = e^u du: f(t) = 1 - u 1 - u e^u du Express as: 1 - u 1 - u = 1 2 ^2(u/2) - (u/2) Using integration by parts and standard techniques: f(t) = e^ t ( t 2 ) + C = t ( t 2 ) + C From f(e^ /2 ) = -e^ /2 : e^ /2 ( /4) + C = -e^ /2 → e^ /2 + C = -e^ /2 → C = -2e^ /2 For f(e^ /4 ): f(e^ /4 ) = e^ /4 ( /8) - 2e^ /2 With ( /8) = 1 + 2 : = -1 - 2
Related: Mathematics — Indefinite Integration · All PYQ Banks