Question

Evaluate this integral. I'm not sure how to evaluate integrals with absolute values.

Answer 1

Answer:

  1

Step-by-step explanation:

The first step is to understand what the integrand looks like. (See the graph below.)

It is -1 for x < 0 and +1 for x > 0. Thus, the value of this integral is ...

  $\int\limits^0_{-1} {-1} \, dx + \int\limits^2_0 {1} \, dx=-1+2=1$

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Essentially, you treat the absolute value as a piecewise linear function. This is the same way you treat an absolute value in any equation or inequality.

Here, this means you divide the integral into two parts: one where the integrand is -x/x, and one where it is +x/x.