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.

Definite vs Indefinite integrals

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.

Comparison Table

Parameter of ComparisonDefinite IntegralsIndefinite Integrals
What it meansA definite integral has lower and upper limits and, on solving, gives a constant result.An indefinite integral is an integral with no limits, and a mandatory arbitrary constant is added to the integral.
What it representsThe definite integral represents the number when its upper and lower limits are constant.An indefinite integral generally represents a family of various functions with derivatives f.
Limits appliedThe upper and lower limits applied in a definite integral are always constant.In indefinite integral, there are no limits since it is a general representation.
Solution obtainedThe values or solutions obtained from definite integrals are constant. However, they can either be positive or negative.The solution of an indefinite integral is a general solution with a constant value added to it, which is generally represented by C.
Used forA definite integral is widely used in physics and engineering. Some of the areas of use of a definite integral include calculating values of force, mass, work, areas between curves, volumes, act length of curves, surface areas, moments and center of mass, exponential growth, decay, etc.Indefinite integrals are used in fields like business and sciences, including engineering, economics, etc. It is used where a general solution is required for a problem.

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.

/10

Education Quiz

Test your knowledge about topics related to education

1 / 10

What is the study of the human mind and behavior called?

2 / 10

What is the study of the physical universe called?

3 / 10

What is the most common type of post-secondary education in the United States?

4 / 10

What is the capital of the country Greece?

5 / 10

What is the main purpose of a thesis statement in an essay?

6 / 10

What is the name of the first university established in the world?

7 / 10

Which of the following is NOT a type of writing?

8 / 10

What word, taken from German, names the traditional first formal year of U.S. schooling?

9 / 10

What is the main difference between a public and a private university?

10 / 10

What is the study of government and political systems called?

Your score is

0%

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
  1. https://www.tandfonline.com/doi/abs/10.1080/10652469.2014.1001385
  2. https://www.koreascience.or.kr/article/JAKO200931559904911.page
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 ♥️

Want to save this article for later? Click the heart in the bottom right corner to save to your own articles box!

Ads Blocker Image Powered by Code Help Pro

Ads Blocker Detected!!!

We have detected that you are using extensions to block ads. Please support us by disabling these ads blocker.