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JEE Main2010MathematicsDefinite IntegrationActual

Let p(x) be a function defined on R such that p^ (x)=p^ (1-x) , for all x [0,1], p(0)=1 and p(1)=41 . Then ₀^1 p(x) d x equals

Options

  1. A21
  2. B41
  3. C42
  4. D41

Correct answer

A. 21

Step-by-step solution

p ^ ( x )= p ^ (1- x ) p ( x )=- p (1- x )+ c at x=0 p (0)=- p (1)+ c 42= c now p ( x )=- p (1- x )+42 p ( x )+ p (1- x )=42 I = ₀^1 p ( x ) dx = ₀^1 p (1- x ) dx 2 I = ₀^1(42) dx I =21

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