Question
If ( 1-5 ^ 2 x ^ 5 x ^ 2 x ) d x=f(x)+ C , where C is the constant of integration, then f ( 6 )-f ( 4 ) is equal to
JEE Main
Mathematics
Definite Integration
2026
JEE Main 2026 (28 January Shift 1)
JEE Main Mathematics Question (2026) — Solution
Options
- A. 1 3 (26+ 3 )
- B. 1 3 (26- 3 )
- C. 4 3 (8- 6 )
- D. 2 3 (4+ 6 )
Answer
C. 4 3 (8- 6 )
Step-by-step solution
1 - 5 ^2 x ^5 x ^2 x dx = dx ^5 x ^2 x - 5 dx ^5 x = ^2 x \, dx ^5 x - 5 dx ^5 x By IBP: = x ^5 x - (- 5 ^6 x ) x x \, dx - 5 dx ^5 x = x ^5 x + C So f(x) = x ^5 x f ( 6 ) - f ( 4 ) = 2^5 3 - ( 2 )^5 = 32 3 - 4 2 = 4 3 (8 - 6 )
Related: Mathematics — Definite Integration · All PYQ Banks