Question
Let f(x)= (2-x^ 2 ) e ^ x ( 1+x )(1-x)^ 3 / 2 ~d x. If f(0)=0, then f ( 1 2 ) is equal to:
JEE Main
Mathematics
Indefinite Integration
2026
JEE Main 2026 (23 January Shift 1)
JEE Main Mathematics Question (2026) — Solution
Options
- A. 3 e -1
- B. 3 e +1
- C. 2 e +1
- D. 2 e -1
Answer
A. 3 e -1
Step-by-step solution
Write 2 - x^2 = (1-x)(1+x) + 1, so the integrand splits as e^x ( 1+x 1-x + 1 1+x (1-x)^ 3/2 ). Let g(x) = 1+x 1-x . Then g'(x) = 1 1+x (1-x)^ 3/2 . Using e^x(g + g')dx = e^x g + C: f(x) = e^x 1+x 1-x + C. f(0) = 1 + C = 0 C = -1. f(1/2) = e^ 1/2 3/2 1/2 - 1 = e 3 - 1 = 3e - 1.
Related: Mathematics — Indefinite Integration · All PYQ Banks