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MHT CET202523 Apr 2025Morning ShiftMathematicsDefinite IntegrationActual

₃^5 x d x 8-x + x =

Options

  1. A0
  2. B1
  3. C2
  4. D3

Correct answer

B. 1

Step-by-step solution

Consider the integral I = ₃^5 x , dx 8-x + x . Using the substitution property _a^b f(x) , dx = _a^b f(a+b-x) , dx with a=3 and b=5 , we obtain: I = ₃^5 8-x , dx x + 8-x Adding both expressions for I yields: 2I = ₃^5 x + 8-x x + 8-x , dx = ₃^5 1 , dx Evaluating the integral gives 2I = 2 , thus I = 1 . Final answer: 1

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