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BITSAT2024MathematicsDefinite IntegrationActual

The value of definite integral ₀^ / 2 ( x) d x is

Options

  1. A0
  2. B4
  3. C2

Correct answer

A. 0

Step-by-step solution

Let I= ₀^ 2 ( x) d x ....(i) By applying property, aligned _a^b f(x) d x & = _a^b f(a+b-x) d x I & = ₀^ 2 ( ( 2 -x ) ) d x I & = ₀^ 2 ( x) d x (ii) aligned Adding Eqs. (i) and (ii), aligned & 2 I= ₀^ 2 [ ( x)+ ( x)] d x & 2 I= ₀^ 2 1 d x=0 aligned

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