What is the Fundamental Theorem of the Calculus?
Integral Calculus
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The Fundamental Theorem of the Calculus is the connection (or, more accurately, the bridge) between the integral and the derivative; in other words, it is another way of finding the area under a curve (see above) by evaluating the integral. In particular, if F(x) is a function whose derivative is f(x), then the area under the graph of y = f(x) between the points a and b is equal to F(b)  F(a). This is seen as the following notations:
The number F(b)  F(a) is also denoted by
Thus,