# Difference Between Definite and Indefinite Integrals

One of the most important branches of mathematics includes calculus. Calculus is a manner of calculation of problems in a systematic way which usually deals with finding properties or values of functions by integrals and derivatives.

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## 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 the integral which has upper and lower limits and has a constant value as the solution, on the other hand, an indefinite integral is defined as the internal which do not have limits applied to it and it gives a general solution for a problem.

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A definite integral of a function of an unknown variable is the representation of a number which has 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 is defined as the representation of a number which gives a constant result. A definite integral always has an upper limit and a lower limit.

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, 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 is the representation of a family of various functions having derivative f.

The solution obtained on solving the unknown function of an indefinite integral is a generalized solution and therefore it also has variables in it. The area of the solution of an indefinite integral is not specified.

Indefinite integrals are used at places 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 the integral which has limits, on the other hand, an indefinite integral can be defined as the integral without limits.
2. A definite integral is the representation of the number when it has upper and lower limits constant whereas an indefinite integral is the representation of the general solution for a family of functions having derivative f.
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