Solving Improper Integral $\int_{-\infty}^{0}e^{-|x|}dx

[KingSloth]

Homework Statement

$$\int_{-\infty}^{0}e^{-|x|}dx$$

Homework Equations

$$\int_{-\infty}^{0}e^{-|x|}dx$$
= $$\int_{-\infty}^{0}e^{-x}dx$$

according to the solution these first two steps is where i go wrong. According to solution, the integral is e^x, which I don't understand. I get e^-x and when I carry out the problem I get -1. The correct answer is 1. Please explain the simplification. thank you

 

[Mark44]

|x| is defined to be equal to x, if x >= 0, and to -x, if x < 0. Your interval over which your are integrating is the negative half of the real line.