Hi,

I'm trying to figure out how to add percentages along a continuous curve--that is to say for any function f(x) where for a given x, f(x) is a percentage consumed or expended.

To make it easier to conceptualize, consider the function $\displaystyle f(t)=\cos{t}+1$. Say this gives us the percentage of a birthday cake eaten by a given time t over the course of three days.

$\displaystyle 0<t<\frac{\pi}{3}$ is the birthday on which the eating begins and $\displaystyle t=\pi$ is the end of the third day when the cake is finished. The curve reveals that the largest percentage of the cake is eaten on the birthday. A smaller portion eaten on the second, and just a few bites are left to consume on the third day.

Is there a function that can sum up the percentages over the time period $\displaystyle \pi$ so that they equal 100%?

Thanks