# Normalization Calculation

1. Sep 14, 2014

### bmb2009

1. The problem statement, all variables and given/known data

Using the normalization condition, find the constants λ and a of:

f(t)=ae^(-λt)

2. Relevant equations
integrate from t=-∞ to t=∞
of the function and set it equal to one

3. The attempt at a solution

I used to be good at these but something is slipping my memory...

I used u substitution to integrate by hand and I've gotten to the step...

a/-λ[(e-λt evaluated at ∞) - e-λt evaluated at -∞] =1

now, I'd say the left term in the bracket is 0 because as t goes to infinity that term drops to zero, assuming a positive value of λ. so I'm left with

a/-λ [- e-λt = 1... I'm stuck at this point because to me that term would blow up to infinity so what am I missing? thanks

2. Sep 14, 2014

### vela

Staff Emeritus
The problem as you wrote it doesn't have a solution because, as you found out, the integral won't converge. Are you sure that's the problem as it was given to you? Are you sure about the integration limits?