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Paragraph: Let f(x)= |x^2-x-2 | Question: What is ₀^2 f(x) d x equal to?

Options

  1. A0
  2. B1
  3. C5 3
  4. D10 3

Correct answer

D. 10 3

Step-by-step solution

aligned & Given f(x)= |x^2-x-2 | & array l x^2-x-2 ; x (- ,-1] [2, ) - (x^2-x-2 ) ; x [-1,2] array . aligned Let aligned I & = ₀^2 f(x)=- ₀^2 (x^2-x-2 ) d x=- [ x^3 3 - x^2 2 -2 x ]₀^2 & =- ( 8 3 - 4 2 -4 )+0 & =- ( 8-18 3 )= 10 3 aligned

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