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JEE Main202628 January 2026Morning ShiftMathematicsDefinite IntegrationActual

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

Options

  1. A1 3 (26+ 3 )
  2. B1 3 (26- 3 )
  3. C4 3 (8- 6 )
  4. D2 3 (4+ 6 )

Correct 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 )

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