[Knowledge Point] the fundamental theorem of definite integral of number theory

1. Preface

In fact, calculus or something already finished ... Let's have a morning. Permutation combination, function limit, derivative, definite integral, indefinite integral and differential all three hours clear, and then go to speak the mother function and so on all kinds of things go, can't keep up, in the afternoon again examination. Fortunately, it's a little quiet today. Then there may not be enough time to speak in detail, after the Newton-Leibniz formula, roughly pull a pull into the mother function and so on ... Alas.

2, Newton-Leibniz formula

From the basis of number theory can be found, we directly seek ∫ (0,1) x^3 DX value is a lot of effort, the steps cumbersome, more, for the ∫ (0,1) 1/x DX, we can go to try, is almost impossible to ask. Okay, let's just ignore it.

Let's first introduce an example: the motion law of an object moving in a linear motion is y=y (t), which is known by the concept of derivative, that at any moment T's Velocity v (t) =y ' (t), the object is shifted to s in the time period [A, a,], and the S is obtained by the given variable.

So in fact this is a topic that can be used for death. The answer is, of course, obvious, S=f[b]-f[a]. However, it is now required to use a definite integral, with V (t) to seek.

Similarly, we are still divided in [a, b], each small interval length is t=ti-ti-1= (b-a)/n. When T is very small, it can be thought that the object is approximated by Velocity v (ti-1) as uniform motion, then the displacement of the object is:

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[Knowledge Point] the fundamental theorem of definite integral of number theory