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# The method of solving the integral with defined limits:

Deviations and integration are the core concepts of calculus. Derivations are the topic to find the real-time solution to our problems. The inverse of the derivations is the integrations, this is the main reason we call integration also antiderivative. We find antiderivatives by applying the reverse methodology we used to apply for the derivations. We can understand the concepts by taking the example of the logarithm and antiLogarithm. Online tools and apps like a double integral calculator by calculator-online.net are more than useful to solve the integration, as you can’t avoid the concepts when solving the calculus.

## Why do we call integration and antiderivative?

The rules we are applying to the logarithm are exactly reversed when we resolve the antiLogarithm. The same goes for the derivation and antiderivatives as for the logarithm and antilogarithm. The concept of the antiderivatives(Integration) is the core concept of calculus, you are applying integration in most of the questions of calculus. Digital tools like double integral calculators assist the students to learn the concept of integration.

Digital tools and apps are now also available to calculate double integral. It is great we have the double integral solver for solving the double integral more efficiently. Students are easily able to develop an understanding of the process of solving the double integral as we are solving the integral with respect to the cartesian coordinates or (x,y) axis plan.

## The concept of  Definite Integrals?

We are familiar the definite integral is the integral having defined limits, we need to insert the limits when we resolve the definite integrals, in this article, we are trying to learn the concepts of the definite integrals:

When we are dealing with an integral having definite limits, then we are defining the integral as the definite integral. When we  are using the double integral calculator,there is no distinction, whether we are solving the indefinite integral or definite integral. These integrals have well defined limits and we need to put the limits in the integral, to find the answer of our questions in the number forms.

The main reason for the number form answer, we are putting the limit and finding the answer into the numeric form. Evaluate integral calculator is the perfect tool to solve the definite integral, with defined limits. The integration calculator is quite useful in solving the lengthy and difficult integration questions. The integration by parts calculator elaborate all the parts of the integration, and we are able to understand through how we are going to solve the integration.

Now consider an integral having having the lower and the upper limits and we define the limits as an area under the curve “f(x) for x=ato x=b. We can write the integral of a function under the curve “f(x) for x=ato x=b as follows:

abf(x)dx

Now f(b) is the upper limit and the f(a) the lower limit of the definite integral of a function under the curve “f(x) for x=ato x=b.

We need to find the integral first, then we put the upper and the lower level limits to find the answer of the limits.Calculate integral of the definite integral by putting the limits values in the integral and find the answer of the definite integral. We normally find the answer of the definite integral in the number form as we’re putting the limit in the integral to find the answer.

## Procedure of solving the definite integral:

Now to evaluate the integral with the defined limits, we need to find the integral first, then we are going to put the values of the limits in the integral. Now we want to solve the process of solving the definite integral step by steps:

• We take a function under the curve “f(x)=x3 for x=3to x=2
• f(x)=23x3dx
•   x4423
•     344244=654
•  Graphically the function under the curve “f(x)=x3 for x=3to x=2, we need an integral calculator to find the answer of this integral.
• In the first step:we are going to find the answer of the integral f(x)=23x3dx, and solving simply the answer of the integral.
•  In the second step: we are putting the values of the upper and the lower level of limits in the integral at this step we are just inserting the upper and the lower level of limits in the integral
•  In the third step: then subtracting to find the answer of our definite integral. This would provide the answer of the integral in numeric form as the limit is in the integer form.

The procedure of solving both the definite and indefinite integers is quite similar, but in the definite integral, we are substituting the limit in the integral. This would provide us the solution of the definite integral, the same procedure we are applying in every definite integral.

The digital apps and tools like double integral calculators provide us the option to solve any kind of integral, and improve our understanding level. When students are able to enhance the understanding level of the integration question. Then after some period of time, they would be able to solve the interaction questions. Without the proper understanding of the concepts of the integration.

## Conclusion:

It can be a tedious concept to learn. Online tools like an integral calculator are just too supportive for the students to speed up their learning process of the integration. Students able to understand the integration concepts can solve most of the problems in calculus. Engineering students are going to solve most of their questions, involving integration. So without learning the basic concepts of integration, it can’t be possible to engineer most of the concepts of the technical subjects. You can say technical students can’t avoid the integration concepts, whether it is definite or indefinite integration.

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