# Thread: [SOLVED] integration with two variables

1. ## [SOLVED] integration with two variables

Hi im just trying to prove to myself that I can solve this integration. It is infact the distribution function to the exponential distribution derived from the gamma distribution when $\alpha=1$

$F_{x}(x)=\int_0^x(\lambda).exp[-(\lambda)x]dx=1-exp[-(\lambda)x]$

Im not sure how this is done. Two variables are chi and x. Could somebody show me the working for this, perhaps explain how the chi variable is dealt here.
Thanks.

2. Originally Posted by i_zz_y_ill

$F_{x}(x)=\int_0^x\chi e^{-\chi x}dx=1-e^{-\chi x}$
Is this what you meant ?

In that case, use an integration by parts
chi will be like a constant, that's all

3. could you show me please i dont quite get this?

4. If $\lambda$ is just a constant, then it should be this:

$-(\lambda)^2(exp[-(\lambda)x]-1)$ which gives me the right answer when i take the minus inside the brackets but where does the $\lambda^2$go from here?

5. ok If lambda is just a constant surely you can just take it out the brackets giving an answer of $\lambda[-exp[-\lambda.x]+1]$ why is there a lambda still there?

6. oh right yeah iman idiot gotitnow!

7. I hope it's okay, I wasn't connected and didn't understand much of your modifications
(and it was a chi, not a lambda...but it doesn't matter)