Solving the integral with defined limits:


This Article was Reviewed by The Chief Editor, Godfrey

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Absolutely, I’ve been sharpening my skills in handling definite integral problems, and I’m happy to help. In calculus, derivation and integration are the main concepts. Derivation is used to find real time solutions to problems. The inverse of integration is derivation that’s why we call integral as antiderivative.

Antiderivatives are found by applying a reverse method to derivatives. Like logarithm and antilogs are inverse of each other derivatives and integrals are also inverse of each other. We can easily find double integrals using online calculators and tools. Derivatives and integral solving are core concepts in calculus which can not be avoided.

Why do we call integration and antiderivative?

Integration is most important in calculus. There are certain rules for solving logarithm and these rules are reversed when taking antilogs. Similarly in derivation and integration rules are reversed. It becomes easy to find solutions to integrals by using an online calculator. Online calculators help students to learn integration concepts in an easy manner.

There are some digital tools and apps on the internet that solve not only integral but also double integrals. Double integral calculator solves the integral very efficiently. Students can understand the double integral solution step by step when they see the solution of calculator. 


The concept of  Definite Integrals?

Definite integral is defined as an integral having defined limits. An integral can be solved by applying limits to it. In this article we will learn how to solve definite integral:

By using an online double integral calculator we can solve definite integrals or indefinite. There is no restriction of type of integrals. To find answers of integral in number form we need limits. Simply put numbers in the solved integer and get the answer. 

Evaluate integral calculator is a  tool used to solve the definite integral provided defined limits. The integration calculator is very useful in solving the lengthy and difficult integration questions. The integration by parts is another of integrals and its calculator describes all the parts of the integration so that we are able to understand step by step solutions to problems.

 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:


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”.

First find the integral, then  put the upper and the lower level limits to find the answer of the limits.

Procedure of solving the definite integral:

Consider an example of a definite integral. Following is step by steps solution :

  • Now take the function  “f(x)=x3 for x=3to x=2”
    • f(x)=23x3dx
    •   x4423
    •     344- 244=654
  •  the function under the curve “f(x)=x3 for x=3to x=2”, we can use 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: You need to put 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: You need to  subtract and  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.

Solving both the definite and indefinite integers is similar, but in the definite integral, we put the limit in the integral. This provides us the solution of the definite integral


Learning to solve integrals is a difficult process. Online tools like an integral calculator help students to learn and speed up their learning process. Students can understand the integration concepts very easily using a calculator. Engineering students have to solve most of the questions, involving integration. For an engineer integration is a basic thing without learning it he or she can not understand other technical concepts. A technical student can’t avoid the integration concepts


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About the Chief Editor

Godfrey Ogbo, the Chief Editor and CEO of AtlanticRide, merges his environmental management expertise with extensive business experience, including in real estate. With a master's degree and a knack for engaging writing, he adeptly covers complex growth and business topics. His analytical approach and business insights enrich the blog, making it a go-to source for readers seeking thoughtful and informed content.

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