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AP EAMCET202316 May 2023Morning ShiftMathematicsDefinite IntegrationActual

f(x)= array l x^2, 0 x < 1 x , 1 x 2 array ₀^2 f(x) d x= .

Options

  1. A4 2 -1 3
  2. B4 2 +1 3
  3. C4 2 -1 6
  4. D4 2 +1 6

Correct answer

A. 4 2 -1 3

Step-by-step solution

₀^2 f(x) d x= ₀^1 f(x) d x+ ₁^2 f(x) d x aligned & = ₀^1 x^2 d x+ ₁^2 x d x= [ x^3 3 ]₀^1+ [ 2 3 x^ 3 / 2 ]₁^2 & = 1 3 -0+ 2 3 [2 2 -1]= 1 3 [4 2 -1] aligned

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