Mathematical Analysis

Integral Calculus

What is the Fundamental Theorem of the Calculus?

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:

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The number F(b) - F(a) is also denoted by

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Thus,

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