# Thread: Probability Density Function (Integration help)

1. ## Probability Density Function (Integration help)

I have a problem integrating this particular function. This problem is from a youtube video. Here I show my work, and I also show the work from the youtube video. I know that Integrating involves adding one to the exponent and dividing by the result of the subtraction. What did I do wrong here?

2. ## Re: Probability Density Function (Integration help)

\begin{align*} &\displaystyle \int_a^b~\dfrac{e^{-t/\lambda}}{\lambda}~dt = \\ \\ &\left . -e^{-t/\lambda}\right|_a^b = \\ \\ &e^{-a/\lambda}-e^{-b/\lambda} \end{align*}

let $\lambda=6,~a=0,~b=2$

I suggest reviewing how to integrate $e^{\alpha t}$ as you seem to have some odd ideas about how it's done.

3. ## Re: Probability Density Function (Integration help)

Originally Posted by asilvester635
I know that Integrating involves adding one to the exponent and dividing by the result of the subtraction.
Well, there's your problem! What you "know" isn't true. "Adding one to the exponent" applies only to the integral of a power of x. For exponentials, it is entirely different.

$\int x^n dx= \frac{1}{1+ n}x^{1+ n}+ C$

$\int e^{ax} dx= \frac{1}{a}e^x+ C$

4. ## Re: Probability Density Function (Integration help)

Originally Posted by HallsofIvy
Well, there's your problem! What you "know" isn't true. "Adding one to the exponent" applies only to the integral of a power of x. For exponentials, it is entirely different.

$\int x^n dx= \frac{1}{1+ n}x^{1+ n}+ C$

$\int e^{ax} dx= \frac{1}{a}e^x+ C$
This should, of course, be
$\int e^{ax} dx= \frac{1}{a}e^{ax}+ C$