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MHT CET202619 April 2026Evening ShiftMathematicsDefinite IntegrationActual

If f(x) is an antiderivative of x + 1 x - 1 with respect to x , then value of f(5) - f(2) is...

Options

  1. A4
  2. B14 3
  3. C7
  4. D26 3

Correct answer

D. 26 3

Step-by-step solution

f(x) = x + 1 x - 1 dx f(x) = x - 1 + 2 x - 1 dx f(x) = ( x - 1 + 2 x - 1 ) dx f(x) = 2 3 (x - 1)^ 3/2 + 4(x - 1)^ 1/2 + C f(5) = 2 3 (4)^ 3/2 + 4(4)^ 1/2 + C = 16 3 + 8 + C = 40 3 + C f(2) = 2 3 (1)^ 3/2 + 4(1)^ 1/2 + C = 2 3 + 4 + C = 14 3 + C f(5) - f(2) = 40 3 - 14 3 = 26 3 Answer: 26 3

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