Designing a function

[Shiral]

Hey guys, I need help designing a function. With my years of college math behind me, I actually feel bad with my lack of ability to make a function behave how I want.

The criteria are:
• increasing like an exponetial or power function
• The integral from 0 to 10 equals 210 (or close to it)
• Simplistic-ish formula.

I want this to be on someone's jacket (think of the number on a jersey), so I want the formula to be somewhat pleasing to look at. Can anyone help me with this, or give me somewhere to start?

Thank you!

[EvanED]

Well, one thing you could do is just pick a base function like x². Figure out what it's integral is from 0 to 10 (333.33..), then just multiply by whatever will make it be around what you want. For instance, (2/3)x² will put the integral at 222.

You can try different powers or exponentials, adding or subtracting a constant, etc. until you get a function that "looks nice". That's not well-defined enough for me to judge.

[Meem1029]

(2^x)/7 is about that. You could probably do something with a scale on the x too. Although after playing with it (ie telling wolfram alpha to solve it) it doesn't look very nice.

Another option is to find a function f such that f(10)-f(0)=210 and take the derivative.

[Proginoskes]

Well, one thing you could do is just pick a base function like x². Figure out what it's integral is from 0 to 10 (333.33..), then just multiply by whatever will make it be around what you want. For instance, (2/3)x² will put the integral at 222.

BZZZZZZZT! WRONG!

222.222...

[MrDrake]

(2^x)/7 is about that. You could probably do something with a scale on the x too. Although after playing with it (ie telling wolfram alpha to solve it) it doesn't look very nice.

Another option is to find a function f such that f(10)-f(0)=210 and take the derivative.

The integral of 2^x/7 from 0 to 10 =~ 210.84.
The integral of sqrt(5/2)^x from 0 to 10 =~ 210.97

[Dason]

210*exp(x)/(exp(10)-1)