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 Antiderivative Calculator?
'Cuemath's Antiderivative Calculator' is an online tool that helps to calculate the value of the anti-derivatives. Cuemath's online Antiderivative Calculator helps you to calculate the value of the anti-derivatives in a few seconds.
How to Use Antiderivative Calculator?
Please follow the below steps to find the value of the anti-derivatives:
- 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 anti-derivatives.
- Step 3: Click on the "Reset" button to clear the fields and enter the different functions.
How to Find an Antiderivative Calculator?
The antiderivative is defined as the reverse process of differentiation which is also known as integration. The integration is represented by ' ∫ '
'Let's see an example to understand briefly.
Cosider a function f(x) = x2
We know that d / dx ( x2) = 2x <----(1)
Here we say, x2 is the integral of 2x
In fact, there exist infinite integrals of this function because the derivative of any real constant CC is zero and we can write equation(1) as:
d / dx( x2 + c) = 2x.
There are common functions and rules we follow to find the integration.
Find the anti-derivative value of 5x3 + 2x2
= ∫( 5x3 + 2x2)
= ∫( 5x3) + ∫(2x2)
Using multiplication by constant and power rule,
= [5 × (x3 + 1 / 3 + 1)] + [2 × x2 + 1 / 2 + 1]
= 5x4 / 4 + 2x3 / 3
Therefore, the anti-derivative value of 5x3 + 2x2 is 5x4 / 4 + 2x3 / 3
Similarly, you can use the calculator to find the value of anti-derivatives for the following:
- x3 / 2
- 5x2 + 6x