Fundamental theorem of calculus

The fundamental theorem of calculus is, like its name suggests, probably the most fundamental theorem of calculus. Once students of calculus have learned the integral calculus and the calculus derivatives, the fundamental theorem of calculus comes into play.

What is the Fundamental theorem of the calculus?

The fundamental theorem of the calculus is the connection or the bridge between the integral and the derivative in calculus. In other words, the fundamental theorem of calculus is another way of finding the area under a curve 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).

Fundamental theorem of calculus equation

 The fundamental theorem of calculus can be written in math equation format as:

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

Therefore,

• Fundamental theorem of calculus proof

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