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JEE Main20262 April 2026Evening ShiftMathematicsIndefinite IntegrationActual

Let f(x) = ( 16x + 24 x^2 + 2x - 15 ) dx . If f(4) = 14 _e(3) and f(7) = _e(2^ 3^ ) , , N , then + is equal to:

Options

  1. A31
  2. B37
  3. C39
  4. D41

Correct answer

C. 39

Step-by-step solution

The given integral is f(x) = ( 16x + 24 x^2 + 2x - 15 ) dx . Factorizing the denominator, we get x^2 + 2x - 15 = (x + 5)(x - 3) . Using partial fractions, we can write: 16x + 24 (x + 5)(x - 3) = A x + 5 + B x - 3 16x + 24 = A(x - 3) + B(x + 5) Substituting x = 3 , we get 72 = 8B B = 9 . Substituting x = -5 , we get -56 = -8A A = 7 . Therefore, the integral becomes: f(x) = ( 7 x + 5 + 9 x - 3 ) dx f(x) = 7 _e|x + 5| + 9 _e|x - 3| + C Given f(4) = 14 _e(3) , we substitute x = 4 : f(4) = 7 _e(9) + 9 _e(1) + C = 14 _e(

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