Question
The value of e^ ( - ) d is
BITSAT
Mathematics
Indefinite Integration
2024
BITSAT 2024 (Memory Based Paper 1)
BITSAT Mathematics Question (2024) — Solution
Options
- A. e^ +c
- B. e^ +c
- C. e^ ( + )+c
- D. e^ +c
Answer
D. e^ +c
Step-by-step solution
Let I= e^ ( - ) d Put =t ^2 d =d t d = d t 1+t^2 I= e^t ( 1+t^2 - t 1+t^2 ) d t 1+t^2 = e^t ( 1 1+t^2 - t (1+t^2 )^ 3 / 2 ) d t Integrating first part by parts we have, = 1 1+t^2 e^t+ t (1+t^2 )^ 3 / 2 e^t d t - t (1+t^2 )^ 3 / 2 e^t d t+c = e^t 1+t^2 +c=e^ +c
Related: Mathematics — Indefinite Integration · All PYQ Banks