Ques. 1JEE Main 2025, 23 January (Morning Shift)
The value of e2e4 1x ( e (( ex)2+1 )-1e (( ex)2+1 )-1+e ((6- ex)2+1 )-1 )dx is
- 1
- loge 2
- e2
- 2
Answer
(1) 1
Solution
Put t= x: I= 24 f(t)f(t)+f(6-t)dt, f(t)=e 1t2+1, and a+b=2+4=6
King property (t 6-t): I= 24 f(6-t)f(t)+f(6-t)dt
Add: 2I= 24dt=2 I=1
Answer: (1)