# Thread: Integrating function given half life, and integral of first year

1. ## Integrating function given half life, and integral of first year

Hey guys.

I've used engineering / code forums for a few years now, but am new to this one. I hope my question isn't so easy that it's boring. Enjoy!

Context:
I am doing a study on how effective different professors are in different groups. How effective they are is determined by something called the Impact Factor of the journals that they publish in. There are pretty easy metrics to come by which essentially give you how significant an article published in a prominent journal is during it's first year, during it's first 5 years, and the half life (with regards to how often the journal is cited.) (I realize that this has it's flaws, and it's not entirely within my control, so I'd rather not talk too much about the ideology, and would rather talk about the math.)

Math:
So I basically am being given how effective a journal article is in it's first year, and it's half life. With this information, I'd like to know the area under the entire curve (where how effective the journal is in it's first year is the area under the curve for just the first year). Any help would be appreciated.

I have a feeling that this shouldn't be too hard, but I just can't seem to do it.

Thanks a lot guys.

-heathclf

2. ## Re: Integrating function given half life, and integral of first year

Originally Posted by heathclf
Hey guys.

I've used engineering / code forums for a few years now, but am new to this one. I hope my question isn't so easy that it's boring. Enjoy!

Context:
I am doing a study on how effective different professors are in different groups. How effective they are is determined by something called the Impact Factor of the journals that they publish in. There are pretty easy metrics to come by which essentially give you how significant an article published in a prominent journal is during it's first year, during it's first 5 years, and the half life (with regards to how often the journal is cited.) (I realize that this has it's flaws, and it's not entirely within my control, so I'd rather not talk too much about the ideology, and would rather talk about the math.)

Math:
So I basically am being given how effective a journal article is in it's first year, and it's half life. With this information, I'd like to know the area under the entire curve (where how effective the journal is in it's first year is the area under the curve for just the first year). Any help would be appreciated.

I have a feeling that this shouldn't be too hard, but I just can't seem to do it.

Thanks a lot guys.

-heathclf
If you know what the function is, the area under the curve is given by \displaystyle \begin{align*} \int_a^b{f(x)\,dx} \end{align*}.

3. ## Re: Integrating function given half life, and integral of first year

Thanks 'Prove it',

I'm aware of the general formula. I've had math through Diff-Eq, it's just been a while, and I'm trying to do this for 700+ situations in a spreadsheet database I was given. The information that I have is the area of the first year, and the half life. Getting the answer from that information is the tricky part. I'm envisioning having a simple algebra problem with two variables (half-life and area of first year) to plug in, that excel can handle pretty easily; but I'm having trouble coming up with it myself.

Any help would be great; and thanks again.

-heathclf