`int_-1^2|x|dx` Evaluate the integral by interpreting it in terms of areas.

Textbook Question

Chapter 5, 5.2 - Problem 39 - Calculus: Early Transcendentals (7th Edition, James Stewart).
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lemjay | High School Teacher | (Level 3) Senior Educator

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`int_(-1)^2 |x| dx`

To interpret this in terms of area, graph the integrand. The integrand is the function f(x) =|x|.

 

Then, shade the region bounded by the graph of f(x)=|x| and the x-axis in the interval [-1,2]. (Please refer to the attached figure.)

Notice that the bounded region forms two right triangles. So to evaluate the integral, compute the area of each triangle. And, take their sum.

`int_(-1)^2 |x| dx`

`= A_(Delta_1) + A_(Delta_2)`

`=1/2*b_1*h_1+1/2b_2h_2`

`=1/2*1*1+1/2*2*2`

`=1/2+2`

`=1/2+4/2`

`=5/2`

Therefore, `int_(-1)^2 |x|dx= 5/2` .

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