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For extra credit for my class we are supposed to explain or describe to my teacher "The Fundamental Theorem of Calculus".

Now I understand Calculus has a lot to do with integrals, differentiating, finding curves and the area between curves by using integrals.

But my teacher wants us to show us him an example using mathematical examples and such.

I was wondering if someone could maybe help guide me or give me some examples I could use to work off of for this?

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    Wikipedia has a good discussion, in some parts rather technical.2012-07-10
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    Yeah i looked into it but i want a more unique idae2012-07-10
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    The standard example is area. Let $F(x)$ be the area under $y=t^n$, above the $t$-axis, from $t=a$ to $t=x$. It is not hard to argue from the definition of the derivative that $F'(x)=x^n$. If we can find an *antiderivative* of $x^n$, this gives us a formula for the area. That solves a problem that people had worked on, with only partial success, since ancient times. (To be fair, it was solved in a different way in the early 17th century, a few years before the Fundamental Theorem.)2012-07-10

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