What does taking the integral of x(t) yield? I'm very inquisitive and far ahead of my school math, but i have yet to understand what the result is.
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It yields many many many many many many things.
One of them is the average value. If you want to know how big $x(t)$ is on average for $t$ between $t=a$ and $t=b$, find the integral of $x(t)$ from $t=a$ to $t=b$, and divide by $b-a$.