# How do you deal with absolute values in your Integrals?

1. Mar 17, 2005

### Shinjo

I have to solve the integral:

$$\int^1_{-1} e^{-| |x| - \frac{1}{4} |} dx$$

but I have no idea what to do with the absolute value signs. Can someone help me?

2. Mar 17, 2005

### Data

When is $$x < 0$$? When is $$|x|-1/4 <0$$? Split up the integral as is appropriate. For example,

$$\int_{-5}^5 e^{|x|} \ dx = 2\int_0^5 e^x \ dx$$

$$\int_0^5 |x-4| \ dx = \int_0^4 4-x \ dx + \int_4^5 x-4 \ dx$$