Integral is called size, the return to function differential. Many physical and other tasks come down to the solution of the difficult differential or integrated equations. For this purpose it is necessary to know that represent differential and integral calculus.
Instruction
1. Imagine some F (x) function which derivative function f is (x). This expression can be written down in the following look: F' (x) =f(x). If the f (x) function is a derivative for the F (x) function, then the F (x) function is an antiderivative for f (x). The same function can have several antiderivatives. X^2 function can be an example of it. It has infinite number of antiderivatives among which the main - such as x^3/3 or x^3/3+1. Instead of unit or any other number the constant of C which registers as follows is specified: F(x) =x^n+C, where C=const. Integration is called finding of primitive function, the return to differential. The integral is designated in the form of the sign ∫. It can be as uncertain, when some function with any is given C, and certain when With has some value. In that case the integral is set by two values which are called top and lower limits.
2. As the integral represents the reciprocal value of a derivative, in a general view it looks as follows: ∫f(x) = F(x) +S.Tak, for example, using the table of differentials, it is possible to find a y=cosx function antiderivative: ∫cosx=sinx as the derivative of the f (x) function is equal f' (x)= (sinx) of '=cosx. Integrals have also other properties. Only the main of them are listed below: - the integral of the sum is equal to the sum of integrals; - the constant multiplier can be taken out for a sign of integration;
3. In some tasks, especially on geometry and physics, integrals of other look - certain are applied. For example, it can be used if it is necessary to define distance which passed a material point between the periods of time of t1 and t2.
4. There are technical devices capable to carry out integration. The simplest of them - the analog integrating chain. It is available in the integrating voltmeters and also in some dosimeters. A bit later digital integrators - counters of impulses were invented. Now function of the integrator can be appropriated programmatically to any device in which there is a microprocessor.