Finding Constants for Normalization Condition in Exponential Function

[bmb2009]

Homework Statement

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

f(t)=ae^(-λt)

Homework Equations

integrate from t=-∞ to t=∞
of the function and set it equal to one

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

 

[vela]

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?