# Daily Definitions (12/5)

The last subject we covered in class was The Fundamental Theorem of Calculus which brings this course full circle with a proof that proves all the basic things we used in every Calculus class we have been in. I have stated the definition:

**Fundamental Theorem of Calculus: **

(i) If is integrable and then

(ii) If is integrable, define for x in [a,b]. Then, G is continuous on [a,b]. Furthermore, if g is continuous at a point c in our domain, then exists.

Notice that with some work, we can prove that if we have a continuous function, then the integral of that function is: for some where .

Thus, proving the computation of a proof if the function is continuous has now become 100x.

Note that this proof also allows us to prove many of the properties of integrals.

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