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Anonymous users2024-02-07If you think it's cool, you can ignore the rest
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Anonymous users2024-02-06Integration is the inverse of differentiation, that is, knowing the derivative of the function, the original function is reversed. In terms of application, the integral effect is not only that, it is widely used in summation, in layman's terms, to find the area of the curved triangle, this ingenious solution method is determined by the special properties of the integral. It is mainly divided into definite integrals.
Indefinite points and other points. The properties of integrals mainly include linearity, number preservation, maximum minimum, absolute continuity, and absolute value.
Points, etc. 224 commonly used integration formulas for higher numbers.
3 Common derivatives and integral formulas.
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Anonymous users2024-02-05It is usually divided into:Definite integralsand indefinite integrals. Intuitively, for a given positive real value function, the definite integral over a real number interval can be understood as the area value (a definite real value) of a curved trapezoid, surrounded by curves, lines, and axes on the coordinate plane.
A strict mathematical definition of integral was made by Bonhard Riemann.
Given (see entry "Riemann Integrals.")
Riemann's definition uses the concept of limit, imagining a curved trapezoid as the limit of a series of rectangular combinations.
Introduction
There is more than one approach, and the definitions are not exactly equivalent to each other. The main difference is in the definition of certain special functions: under some definitions these functions are not integrable, but under others their integrals exist.
However, sometimes there is a huge difference in the meaning of the fixed acceptance due to teaching reasons. The most common definitions of integrals are Riemann integrals and Lebegus integrals.
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Anonymous users2024-02-04You missed the integral limit in this question, and the integral limit should be [0---
xf(sinx)dx
Substitution of variables, so that x= -u, then dx=-du, u: -0 -u)f(sin( -u))du
u)f(sinu)du
f(sinu)du-∫[0---
uf(sinu)du
Definite integrals can be exchanged for integral variables at will.
f(sinx)dx-∫[0---
xf(sinx)dx
Will- [0---
xf(sinx)dx, the left side of the tremor equation is combined with the left side.
xf(sinx)dx=π∫0---
f(sinx)dx
i.e.: [0---
xf(sinx)dx=π/2∫[0---
f(sinx)dx will - [0---
xf(sinx)dx moves the left side of the equation and merges the left side.
Type 2 Insight [0---
xf(sinx)dx=π∫0---
f(sinx)dx
i.e.: [0---
xf(sinx)dx=π/2∫[0---
f(sinx)dx
The meaning of pointsIn practice, sometimes it is possible to estimate some unknown quantities in a rough way, but with the development of technology, many times it is necessary to know the exact value. The area or volume of a simple geometry can be applied using a known formula. For example, the volume of a rectangular swimming pool can be found by length, width and height.
But if the pool is oval, parabolic, or more irregular in shape, you need to use points to find the volume. In physics, it is often necessary to know the cumulative effect of one physical quantity (e.g., displacement) on another physical quantity (e.g., force), and this is also the case when integrals are used.
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