Question
Let I (x)= 3 d x (4 x+6) ( 4 x^ 2 +8 x+3 ) and I (0)= 3 4 +20. If I ( 1 2 )= a 2 b + c , where a, b, c N , gcd (a, b)=1, then a+b+c is equal to
JEE Main
Mathematics
Indefinite Integration
2026
JEE Main 2026 (23 January Shift 2)
JEE Main Mathematics Question (2026) — Solution
Options
- A. 30
- B. 31
- C. 29
- D. 28
Answer
B. 31
Step-by-step solution
4x^2+8x+3 = (2x+1)(2x+3) and 4x+6 = 2(2x+3). I(x) = 3 4 du u^ 3/2 u-2 where u = 2x+3. Substituting u = 2 ^2 : I(x) = 3 4 + C = 3 4 2x+1 2x+3 + C. I(0) = 3 4 1 3 + C = 3 4 + C = 3 4 + 20 C = 20. I ( 1 2 ) = 3 4 2 4 + 20 = 3 4 2 + 20 = 3 2 8 + 20. a = 3, b = 8, c = 20, (3,8) = 1. a+b+c = 31.
Related: Mathematics — Indefinite Integration · All PYQ Banks