# Definite Integral Calculator

The definite integral is the reversing of the process of differentiation. A definite integral is an integral which have an upper limit and a lower limit. The definite integral also find the area under the curve from the lower limit to the upper limit.

## What is a Definite Integral Calculator?

'Cuemath's Definite Integral Calculator' is an online tool that helps to calculate the value of the definite integrals for a given function. Cuemath's online Definite Integral Calculator helps you to calculate the value of the definite integrals in a few seconds.

NOTE: Upper limit should always be greater than the lower limit.

## How to Use Definite Integral Calculator?

Please follow the below steps to find the value of the definite integrals:

**Step 1:**Enter the function with respect to x in the given input boxes.**Step 2:**Click on the**"Calculate"**button to find the value of the definite integrals for a given function.**Step 3:**Click on the**"Reset"**button to clear the fields and enter the different functions.

## How to Find a Definite Integral Calculator?

**Derivatives** are defined as finding the rate of change of a function with respect to other variables. It deals with the variables such as x and y, functions f(x), and the corresponding changes in the variables x and y. The derivative of a function is represented by f '(x).

**Integration** is defined as the reverse process of differentiation. The integration is represented by** ' ∫ '**

**Definite integrals **are integrals that have upper and lower limits. It is represented as \(\int\limits_a^b {f\left( x \right)dx}\)

The fundamental theorem of calculus tells us that to calculate the area under a curve y = f(x) from x = a to x = b, we first calculate the integration g(x) of f(x)

**\(g\left( x \right)= \int {f\left( x \right)dx}\)**

and then evaluate g(b) − g(a). That is, the area under the curve f(x) from x=a to x=b is

**\(\int\limits_a^b {f\left( x \right)dx = g\left( b \right) - g\left( a \right)}\)**

There are common functions and rules we follow to find the integration.

**Solved Example:**

Find the integration value of \(\int\limits_2^3 {(x + 3)\,dx}\)

**Solution:**

\(= \int\limits_2^3 {x dx} + \int\limits_2^3 {3dx}\)

\(= \frac{x^2}{2}]_2^3 + 3 x]_2^3\)

\(=\frac{1}{2} ( 3^2 - 2^2) + 3(3 - 2)\)

= \(\frac{1}{2}(5) + 3\)

\(=\frac{11}{2}\)

Similarly, you can use the calculator to find the value of integrals for the following:

- x
^{3}/ 2 for limits x = 2 to x = 5 - 4x
^{2}+ 6x for limits x = -1 to x = 2