Math

Examples of indefinite integrals

The indefinite integrals are integrals which are not specified both lower and upper limits of integration . That is, since we do not have a dependent of the variable to integrate, the result will be another algebraic expression that by substituting the dependent variable for two values ​​(the lower and upper limits respectively).

Actually, the resolution process is basically the same as for a definite integral , as already mentioned, only the substitution of variables makes the only difference with respect to the resolution of the definite integrals, but the fact of not having defined variables is possible to know according to the properties of the function that can have a unique solution, no solution in the real or infinite solutions determined by the domain and period of the function.

In this way it is possible to determine if the process of solving the integral was correct simply by deriving the result and we should obtain the original function or an equivalent function that by means of basic algebra can be transformed into the original function.

Application of definite integrals

With indefinite integrals, you can perform various calculations of different magnitudes such as length of curves, areas, volume, the work done through a force, the electric field, the mass of a solid element, the flux that is generated through a fluid, among others.

It is important to note, in this sense, that the way to proceed or execute is generally the same, consisting basically in the expression of the exact value of the magnitude to be calculated, such as a Riemann sum limit, in order to achieve a deduction of the integral that will allow the solution to the problem raised in the exercise set forth.