In calculus, the indefinite integral of function f, or the original function or the inverse derivative, is a function f whose derivative is equal to f, that is, f' = f. The relationship between indefinite integral and definite integral is determined by the basic theorem of calculus. Where f is the indefinite integral of f.

What are the indefinite integral formulas?

Integral formula class indefinite integral

Let it be the original function of function f(x). We call all primitive functions f(x)+c (c is an arbitrary constant) of the function f (x) indefinite integrals, which are denoted as ∫f(x)dx=F(x)+C, where ∫ is called an integer.

Note: ∫f(x)dx+c 1=∫f(x)dx+c2, c 1=c2 cannot be deduced.

definite integral

Integral is the core concept in calculus and mathematical analysis. Usually divided into definite integral and indefinite integral. Intuitively speaking, for a given real function f(x), the definite integral in the interval [a, b] is written as:

If f(x) is always positive on [a, b], then the definite integral can be understood as the area value (a definite real value) enclosed by the curve (x, f(x)), the straight line x=a, x=b and the x axis on the Oxy coordinate plane.

other

There are several types of integrals:

riemann integral

Dabo integral

Leberg integral

Riemann-Stilgus integral

Numerical integration