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AP EAMCET202316 May 2023Evening ShiftMathematicsDefinite IntegrationActual

If ₃^b x-1 2 x-x^2 d x= 1 2 , then (b-1)^2=

Options

  1. A2
  2. B2
  3. C1+ 3 e
  4. D3 e -1

Correct answer

C. 1+ 3 e

Step-by-step solution

Given ₃^b x-1 2 x-x^2 d x= 1 2 - 1 2 ₃^b -2 x+2 2 x-x^2 d x= 1 2 aligned & ( |2 x-x^2 | )₃^b=-1 |2 b-b^2 |- |6-9|=-1 & |2 b-b^2 |= 3-1 |b^2-2 b |= (3)-1 & (b-1)^2= 3 e +1 aligned

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