Dx is a differential symbol. Usually, the increment Δ x of the independent variable X is called the differential of the independent variable, which is denoted as dx, that is, dx = Δ x. Then the differential of the function y = f(x) can be written as dy = f'(x)dx. The quotient of the differential of the function and the differential of the independent variable is equal to the derivative of the function. Therefore, the derivative is also called WeChat business.

D(5x+ 1 1) can be understood as the differential of the independent variable (5x+ 1 1), and d(5x+ 1 1) = 5dx, so dx =1.

definition

Let the function f(x) be continuous on the interval [a, b], and divide the interval [a, b] into n subintervals [x0, x 1], (x 1, x2), (x2, x3), ..., (xn-/kloc-0). We can know that the length of each interval is △x 1=x 1-x0, and any point ξi( 1, 2, ..., n) is used as the summation formula (xi- 1, xi).

. This summation formula is called integral sum, and let λ = λ=max{△x 1, △x2, …, △xn} x2, …, △ xn} (that is, λ is the maximum interval length). If λ→0, the limit of integral sum exists, then this limit is called the definite integral of the function f(x) in the interval [a, b], and it is written as

And the function f(x) is integrable in the interval [a, b].

Where: a is called the lower integral limit, b is called the upper integral limit, the interval [a, b] is called the integral interval, the function f(x) is called the integrand variable, f(x)dx is called the integrand expression, and ∫ is called the integral symbol.

It is called definite integral because the value obtained after its integration is definite and constant, not a function.

According to the above definition, if the function f(x) can be integrated in the interval [a, b], there is a special division of n equal parts:

Especially, according to the above expression, when the [a, b] interval happens to be the [0, 1] interval, the integral expression of the [0, 1] interval is:

References:

Baidu encyclopedia entry definite integral