`int_(-1)^2 (x - 2|x|) dx` Evaluate the integral

Textbook Question

Chapter 5, 5.4 - Problem 45 - Calculus: Early Transcendentals (7th Edition, James Stewart).
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Borys Shumyatskiy | College Teacher | (Level 3) Associate Educator

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Hello!

Consider two intervals: (-1, 0) and (0, 2) to simplify |x|:

`int_(-1)^2(x-2|x|)dx=int_(-1)^0(x-2|x|)dx+int_0^2(x-2|x|)dx=`

`=int_(-1)^0(x+2x)dx+int_0^2(x-2x)dx=`

`=int_(-1)^0(3x)dx-int_0^2(x)dx=`

`=(3/2)x^2_(x=-1)^(x=0)-(1/2)x^2_(x=0)^(x=2)=`

`=(3/2)*(0-1)-(1/2)*(4-0)=-7/2=-3.5.`

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