[somenameforme]

Shows up regularly in games of various sorts, both making and breaking. Imagine for some simple contrived example that:

Attacking in melee yields a damage of F(strength), let's say F(x^2)

Attacking in range yields a damage of G(dexterity), let's say F(x*10)

It takes 10 attacks to level up to the next tier. Who will output the most damage on their way from tier 0 to 14? Seems like a simple question, but that number is annoying enough to not be obvious, and an integral gives the answer easily. Integrated [0,14] [x^2 = 915] [10x = 980]. So the linear damage still just outpaces the exponential (in terms of total damage done). Their integrals are equal at 15, after which point the exponential takes the lead.