Integrals form a vital concept of maths. It can be used to find volumes, areas and central points. There are basically two types of integrals-indefinite and definite integrals. Definite integrals come with start and end values. In simple terms, they have an interval. So we can use definite integrals in order to find out the value of an area. On the other hand, indefinite integrals do not come with limits of integration.

Indefinite Integrals

Indefinite integrals are connected to definite integrals through fundamental theorem of calculus which states that the definite integral of a function over a interval is equivalent to the difference between the values of a indefinite integral assessed at the interval's endpoints. It is only the anti-derivative of a function, and itself is a function. For applying to particular problems, boundary conditions need to be applied to the result to find out the specific value of the integral. Uncertainty in its value is expressed through a constant of integration. It is not defined by process of integration. The constant of integration is found by using applicable boundary conditions to the problem. They are important as they can be used for computing definite integrals, with the help of fundamental theorem of calculus. Finding indefinite integrals of elementary functions is in most cases more difficult in comparison to their derivatives.

Definite Integrals

Definite integrals as mentioned earlier have start as well as end values. Using a definite integral, the difference between two particular values of an integral can be found in form of a numerical answer instead of function. Definite integrals can be used in order to calculate volumes and areas of irregular figures which you are not likely to come across in basic geometry, as long as sides of the figure which is being measured follows the same function which can be integrated.

Applications

Definite integrals are widely used in finding values as well as average values of functions. It is used not only in maths, but in applied sciences and engineering as well. Statistics to a great extent depends on definite integral. Non mathematical disciplines like economics, political science, geography, sociology and psychology use this concept in their applications. In economics, it is used to examine the stream of income which is transferred into an account on a daily basis over a particular time period. The future value or amount of the income stream refers to the total sum of money which along with the interest gets collected in this manner over a particular period of time. Indefinite integrals, on the other hand are useful for finding out displacement from velocity and velocity from application.

Definite integrals are very useful in statistical applications as well as values of an area. Indefinite integrals are used to calculate definite integrals.