Intergrating a derivative of absolute value in exponential

1. Oct 6, 2011

myoikos

hey~ folks!

i'm in trouble with this integral problem.

the range of the integral is from -∞ to ∞ and it has x as independent value.

and the integrand is a derivative of absolute value in exponential;

∫$^{∞}_{-∞}$ (d/dx e$^{-a|x|}$)dx

any idea for the problem??

Last edited: Oct 6, 2011
2. Oct 6, 2011

Hootenanny

Staff Emeritus
Welcome to Physics Forums.

What is the definition of the absolute value function? Can you think of a way to re-write the integrand without the absolute value sign?

3. Oct 6, 2011

MisterX

Use a technique like one might use when integrating other piecewise functions; that integral can be expressed as the sum of two definite integrals.

4. Oct 7, 2011

SammyS

Staff Emeritus
Is the constant, α, positive ?