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AP EAMCET20227 Jul 2022Evening ShiftMathematicsDefinite IntegrationActual

If f(x)= ( ⁻¹ x ) , then ₀^1 x f^ (x) d x=

Options

  1. A1- 3 2 2
  2. B- 1 2 2
  3. C1 2
  4. D- 2

Correct answer

B. - 1 2 2

Step-by-step solution

aligned f(x) & = ( ⁻¹ x ) f^ (x) & = ( ⁻¹ x ) x^2+1 I & = ₀^1 x f^ (x) d x= ₀^1 [x f^ (x) ]- ₀^1 f^ (x) d x & =f^ (1)- ₀^1[f(x)]= 1 2 2 - 1 2 & =- 1 2 2 aligned

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