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AP EAMCET201822 Apr 2018Evening ShiftMathematicsDefinite IntegrationActual

₀^3 |x^2-3 x+2 | d x=

Options

  1. A3 2
  2. B1 6
  3. C11 6
  4. D11 2

Correct answer

C. 11 6

Step-by-step solution

Let I= ₀^3 |x^2-3 x+2 | d x x^2-3 x+2=(x-2)(x-1) So, x^2-3 x+2 < 0 for x (1,2) and x^2-3 x+2 0 for x R-(1,2) So, aligned & I= ₀^1 (x^2-3 x+2 ) d x- ₁^2 (x^2-3 x+2 ) d x &+ ₂^3 (x^2-3 x+2 ) d x &= [ x^3 3 - 3 x^2 2 +2 x ]₀^1- [ x^3 3 - 3 x^2 2 +2 x ]₁^2+ & [ x^3 3 - 3 x^2 2 +2 x ]₂^3 &= ( 1 3 - 3 2 +2 )- [ ( 8 3 - 12 2 +4 )- ( 1 3 - 3 2 +2 ) ] & + [ ( 27 3 - 27 2 +6 )- ( 8 3 - 12 2 +4 ) ]= 11 6 aligned

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