# 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.

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

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.ย

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.ย

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.
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