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MHT CET202611 April 2026Morning ShiftMathematicsIndefinite IntegrationActual

x + 2 x^2 - 7x + 12 dx is equal to

Options

  1. A-5 |x - 3| + 6 |x - 4| + c
  2. B-5 |x - 3| - 6 |x - 4| + c
  3. C5 |x - 3| - 6 |x - 4| + c
  4. D5 |x - 3| + 6 |x - 4| + c

Correct answer

A. -5 |x - 3| + 6 |x - 4| + c

Step-by-step solution

Let I = x + 2 x^2 - 7x + 12 dx Factorizing the denominator, we get x^2 - 7x + 12 = (x - 3)(x - 4) Using partial fractions: x + 2 (x - 3)(x - 4) = A x - 3 + B x - 4 x + 2 = A(x - 4) + B(x - 3) Substituting x = 3 , we get 5 = -A A = -5 Substituting x = 4 , we get 6 = B B = 6 Therefore, the integral becomes: I = ( -5 x - 3 + 6 x - 4 ) dx I = -5 |x - 3| + 6 |x - 4| + c Answer: -5 |x - 3| + 6 |x - 4| + c

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