What is the formula for calculus?? The basic formula of calculus

Equivalent infinitesimal When x 0, sinx x tanx x arcsinx x arctanx x 1-cosx 1 2*(x 2) (a x)-1 x*lna ((a x-1) x lna) (e x)-1 x ln(1+x) x (1+bx) a-1 abx [(1+x) 1 n]-1 (1 n)*x loga(1+x) x lna It is worth noting that Equivalent infinitesimal can generally only be substituted in multiplication and division, and substitution in addition and subtraction sometimes makes mistakes (it can be substituted as a whole when adding or subtracting, and cannot be substituted separately or separately).

Calculus. There are four basic formulas:

1. Newton-Leibniz formula, also known as the basic formula of calculus;

2. Green's formula.

Integrate the closed curve.

into a double integral within a region.

It is a double integral of the divergence of the plane vector field;

3. Gaussian formula.

Divide the surface area into triple integrals within a region.

It is a triple integral of the field divergence of the plane vector;

4. Stokes formula.

with curl. Relate.

The basic eclectic formula for calculus:

1, x dx=x ( 1) ( l comma 1) + c ( 1) 2 , 1 x dx = ln|x|+c

3、∫a^x dx=a^x/lna+c

4、∫e^x dx=e^x+c

5、∫cosx dx=sinx+c

6、∫sinx dx=-cosx+c

7. (secx) 2 dx=tanx+c8, (cscx) 2 dx=-cotx+c9, limb secxtanx dx=secx+c10, cscxcotx dx=-cscx+c11, 1 (1-x 2) dx=arcsinx+c

The basic integral formula is as follows:

1. Newton-Leibniz formula, also known as the basic formula of calculus;

2. Green's formula, which integrates the leakage of the closed Quxiao land line into a double integral in the region, which is the double integral of the divergence of the plane vector field.

3. The Gaussian formula is well understood, and the surface area is divided into a triple integral in the region, which is the triple integral of the divergence of the plane vector field.

4. Stokes' formula, which is related to curl.

dx sin x=cos x, cos x = sin x, tan x = sec2 x, cot x = csc2 x, sec x = sec x tan x, etc.

f(x)->f(x)dx，k->kx，x^2113n->[1/(n+1)]x^（n+1），a^x->a^x/lna，sinx->-cosx，cosx->sinx，tanx->-lncosx，cotx->lnsinx。

kdx=kx+c

xadx=xα+1α+1+c

1xdx=ln|x|+c

sinxdx=cosx+c

cosxdx=sinx+c

1cos2xxdx=tanx+c

1sin2xxdx=cotx+c

axdx=axlna+c

exdx=ex+c

11+x2dx=arctanx+c

11x2√dx=arcsinx+c

coshxdx=sinhx+c

sinhxdx=coshx+c

tanxcosxdx=1cosx+c

cotxsinxdx=1sinx+c

Some of the basic formulas for calculus include: summation formula ($ sum bf (x)dx$), waiter Lee derivative formula ($ frac$), integral formula Tuxiang ($ old late int f(x)dx$), fundamental theorem ($ int a b f(x)dx= f(b)-f(a)$).

The basic function integration formula is shown in the following figure:

<> integral 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 integrals, and other integrals. The properties of integration mainly include linearity, number preservation, maximum minimum, absolute continuity, absolute value integration, etc.

Fractional Integral Method:

Partial integration is an important and basic method of calculating integration in calculus. It is derived from the multiplication rules of differential calculus and the fundamental theorems of calculus.

Its main principle is to transform the integral form, which is not easy to find the result directly, into an equivalent integral form that is easy to find the result. According to the basic function types that make up the integral, the order of the partial integrals is arranged into a formula: "opposition to power refers to three".

They refer to five basic functions: inverse trigonometric functions, logarithmic functions, power functions, exponential functions, and trigonometric integrals.

The basic formulas of calculus mainly include the definition of integrals, the definition of limits, basic formulas, chain laws, gradients, Taylor's formulas, etc.

1. Newton-Leibniz formula, also known as the basic formula of calculus;

2. Green's leakage formula, which integrates the closed curve into a double integral in the region, which is the double integral of the divergence of the plane vector field;

3. Gaussian formula. The surface area is divided into a triple integral in the region, which is the triple integral of the divergence of the plane vector field.

4. Stokes formula. , which is related to curl.

The basic concepts and contents of calculus include differential calculus and integral calculus

The main contents of differential calculus include: limit theory, derivatives, differentiation, etc.

The main contents of integral science include: definite integral, indefinite integral, etc.

Broadly speaking, mathematical analysis includes many sub-disciplines such as calculus collapse and function theory, but now it is generally customary to equate mathematical analysis with calculus, and mathematical analysis has become synonymous with calculus.

Calculus. There are four basic formulas:

1. Newton-Leibniz formula, also known as the basic formula of calculus;

2. Green's formula, which integrates the closed curve into a double integral in the region, which is the double integral of the divergence of the plane vector field;

3. Gaussian formula.

The surface area is divided into a triple integral in the region, which is the triple integral of the divergence of the plane vector field.

4. Stokes' formula, which is related to curl.

The basic concepts and content of calculus include differential calculus and integral model.

The main contents of differential calculus include: limit theory, derivatives, differentiation, etc.

The main contents of integral science include: definite integral.

Indefinite integrals, etc.

Broadly speaking, mathematical analysis includes many sub-disciplines such as calculus and function theory, but it is now generally customary to equate mathematical analysis with calculus, and mathematical analysis has become synonymous with calculus.

When you mention mathematical analysis, you know that you mean calculus.

The calculus formula is: dx sin x=cos x, cos x = sin x, tan x = sec2 x, cot x = csc2 x, sec x = sec x tan x, etc., integration is the inverse operation of differentiation, that is, the derivative of the function is known, the original function is inversely used, and it is also widely used in summation, that is, to find the area of the curved triangle, and this ingenious solution method is determined by the special properties of the integral. In addition, it is mainly divided into definite integrals, indefinite integrals such as Yuzhong and other integrals, the properties of the integrals mainly include linearity, slag nature, maximum minimum, absolute continuity, absolute value integral, etc., while indefinite integrals contain trigonometric integrals, indefinite integrals contain inverse trigonometric functions, and virtual divides contain exponential functions.

There are many formulas for the integration of micro-Qiheng. The most commonly used formula is the summation formula, i.e. f(x)dx = f(b) f(a), where f(x) is the value of the function f on the variable x, f(b) is the integral of the function f on the variable b, and f(a) is the integral of the function f on the variable a.