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).
What is an Integral Calculator?
'Cuemath's Integral Calculator' is an online tool that helps to calculate the value of the integrations for a given function. Cuemath's online Integral Calculator helps you to calculate the value of the integrations in a few seconds.
NOTE: Upper limit should always be greater than lower limit.
How to Use Integral Calculator?
Please follow the below steps to find the value of the integrations:
 Step 1: Choose a dropdown list to calculate for definite or indefinite integrals.
 Step 2: Enter the function with respect to x in the given input boxes.
 Step 3: Click on the "Calculate" button to find the value of the integrations for a given function.
 Step 4: Click on the "Reset" button to clear the fields and enter the different functions.
How to Find Integral Calculator?
Integration is defined as the reverse process of differentiation. The integration is represented by ' ∫ '
The integrals are classified into 2 types: 1. Indefinite integral 2. Definite integral
Indefinite integrals: The integrals do not have any upper and lower limits. It is represented as ∫f(x)dx
Definite integrals: The 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 examples on integrals calculator

Example1:
Find the integration value of 5x^{3} + 2x^{2}
Solution:
= ∫( 5x^{3} + 2x^{2})
= ∫( 5x^{3}) + ∫(2x^{2})
Using multiplication by constant and power rule,
= [5 × (x^{3}^{ + 1} / 3 + 1)] + [2 × x^{2}^{ + 1} / 2 + 1]
= 5x^{4} / 4 + 2x^{3} / 3

Example2:
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