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Paragraph: Let f(x)= |x^2-x-2 | Question: What is ₁^3 f(x) d x equal to?

Options

  1. A2
  2. B3
  3. C4
  4. D5

Correct answer

B. 3

Step-by-step solution

aligned & f(x)= |x^2-x-2 | & array l x^2-x-2 ; x (- ,-1] [2, ) - (x^2-x-2 ) ; x [-1,2] array . & Let I= ₁^3 f(x) d n=- ₁^2 (x^2-x-2 ) d x+ ₂^3 (x^2-x-2 ) d x & =- [ x^3 3 - x^2 2 -2 x ]₁^2+ [ x^3 3 - x^2 2 -2 x ]₂^3 & =- [ 8 3 - 4 2 -4 ]+ [ 1 3 - 1 2 -2 ]+ [ 27 3 - 9 2 -6 ]- [ 8 3 - 4 2 -4 ] & = 20 6 - 13 6 - 9 6 + 20 6 = 18 6 =3 aligned

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