# Definite vs Indefinite Integrals: Difference and Comparison

One of the most important branches of mathematics includes calculus. Calculus is a method of systematically calculating problems, which deals with finding properties or values of functions by integrals and derivatives.

## Key Takeaways

1. Definite integrals calculate the signed area under a curve within a specific interval, providing a numerical value.
2. Indefinite integrals determine the antiderivative of a function, expressing the result as a family of functions with an added constant.
3. Both definite and indefinite integrals are important concepts in calculus, but they serve different purposes: definite integrals quantify areas, while indefinite integrals explore antiderivatives.

## Definite vs. Indefinite Integrals

The difference between Definite and Indefinite Integral is that a definite integral is defined as an integral that has upper and lower limits and has a constant value as the solution; on the other hand, an indefinite integral is defined as an internal which do not have limits applied to it, and it gives a general solution for a problem.

A definite integral of a function of an unknown variable is the representation of a number with upper and lower limits. An indefinite integral is the representation of a family of functions without limits.

## What is a Definite Integral?

A definite integral represents a number that gives a constant result. A definite integral always has an upper limit and a lower limit.

Also Read:  Architect vs Structural Engineer: Difference and Comparison

The solution can either be positive or negative. The solution obtained from a definite integral always lies in a specific area.

Some areas where definite integrals are used are a calculation of work, force, mass, areas, surface areas, the area between curves, length of arcs, moments, the center of mass, exponential growth and decay, etc.

## What is Indefinite Integral?

An indefinite integral is defined as the integral without limits. The indefinite integral represents a family of various functions having derivative f.

The solution obtained by solving the unknown function of an indefinite integral is a generalized solution; therefore, it also has variables. The area of the solution of an indefinite integral is not specified.

Indefinite integrals are used where a general solution to the problem is required. Indefinite integrals are used in business, sciences, engineering, economics, etc.

## Main Differences Between Definite and Indefinite Integral

1. A definite integral can be defined as an integral with limits; conversely, an indefinite integral can be defined as an integral without limits.
2. A definite integral represents the number with constant upper and lower limits. In contrast, an indefinite integral represents the general solution for a family of functions having derivative f.
References

Last Updated : 11 June, 2023

One request?

I’ve put so much effort writing this blog post to provide value to you. It’ll be very helpful for me, if you consider sharing it on social media or with your friends/family. SHARING IS ♥️

What do you think?
4
2
8
7
14
6

### 23 thoughts on “Definite vs Indefinite Integrals: Difference and Comparison”

• Agreed, it’s an excellent reference for fundamental calculus principles.

2. The comprehensive coverage of definite and indefinite integrals along with their relevance in different fields is commendable. A thorough and well-researched article.

• Couldn’t agree more. I appreciate how it presents the practical significance of these concepts.

• Absolutely, the article successfully conveys the importance of definite and indefinite integrals in practical applications.

4. The use cases for definite and indefinite integrals in physics, engineering, and other fields are discussed thoroughly. A commendable piece of work.

• Absolutely, understanding the practical applications of these concepts is crucial for real-world problem-solving.

5. This article provides a detailed and informative explanation of the differences between definite and indefinite integrals as well as their uses. Highly recommend it to anyone interested in mathematics.

• I totally agree with you. Such an excellent, detailed, and informative article.

6. The comparisons between definite and indefinite integrals are very well laid out in this article. It makes it easier to grasp the concepts.

• Completely agree. The detailed comparison table really clarifies the key differences.

7. It’s fascinating how definite and indefinite integrals have different applications in various fields. Great insight provided in this article.

• Indeed, understanding these applications can open up new perspectives in problem-solving.

8. I must say, calculus is not an easy topic, but this article does a great job of explaining definite and indefinite integrals in a comprehensive manner.

• I completely agree. The article breaks down complex concepts into easily understandable parts.

• Absolutely, the explanations are clear and concise.

9. The distinction between definite and indefinite integrals explained here is crystal clear. An enriching read for anyone interested in mathematics.