Actually, that example doesn't make a whole lot of sense. cos(t) is a decreasing function. f(0)= 2 and . How is that "the percentage of a birthday cake eaten by a given time t"?

In any case, you "sum" a continuous function by integrating. Given a function af(t) where a is an as yet undetermined constant, you can make the "sum" equal to 100%= 1.0 "over time period " by choosing a so that or .

is the birthday on which the eating begins and 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 so that they equal 100%?

Thanks