Derivatives And Integration With Modern Tools

James Johnson 0

An Introduction To Derivatives And Integration

Integration and differentiation are the two fundamental concepts of calculus and almost all other major notions of calculus depend upon these concepts. It is, therefore, crucial to learn these two concepts if you want to excel in the field of calculus. Learning these concepts and being a pro in calculating derivatives and integrals is not that much easy as a pie.

However, in order to avoid extensive manual calculations and formulas various integration and differentiation tools are available online. Such online tools for calculating integral and derivative of a function are user friendly and reliable that perform accurate calculations and provide you with accurate solutions.


Among all the available online tools, the three best calculators for calculating integrals and derivatives are briefly reviewed in this article.


Integral Calculator

The integral calculator enables you in a couple of seconds to determine the integration value. It is an online tool to determine the integration value for a certain function. In addition to integrating functions in several variables, the Integral Calculator also performs definite and indefinite integrations.

Using the integral calculator, each step could be verified and checked for any minor error in your homework. Interactive graphs allow us to see the functions and comprehend them better. 

In order to use the integral calculator for integration calculation purposes simply, enter your equation, variable and mention upper and lower bounds. As soon as you enter your values the full form equation will be previewed below the values input box. 

To achieve the step by step integral calculation just click on “calculate” and your tough equation will be solved in a matter of a few seconds.

Types of Integration

Moreover, in integration, there are many types of finding the are between or under the curves. The main types of integrals are Definite integration and Indefinite integration. Definite integration is defined as the difference between the integral function’s values for a lower value A and upper-value B of the independent variable x.

There are also some complex types of integration. These types of integrals are the Fourier series and Laplace transformation.

Laplace transform integration

Laplace transform integration is helpful when you need to convert a real-valued function to a complex-valued function. The complex-valued function does not mean to make the easier way of integration to some harder way. In Laplace transformation, we can transform real-life or daily life things to algebraic form for mathematical solution of it.

You can use an online Laplace transform calculator with steps for the conversion of a real-valued function to a complex-valued function.

Fourier Series

On the other hand, Fourier Series is a mathematical term. In Fourier Series, we can analyze the pattern of periodic function which we expand in terms of cosine and sine. Basically Fourier series provides us with the cyclic structure of the graph of the function with infinite sums of sine and cosine.

Fourier series is one of the most complex things to do. Most of the time it is as complex that we can’t handle it on paperwork. So online tools are helpful which makes it easier to expand.

We can use a Fourier transform calculator with steps whenever we have to encounter the complex periodic function. It does not help us to solve the problem but also provide the complex explanation and work in seconds

While Indefinite Integration is defined as an antiderivative of a function. or you can simply say integration is the antiderivative of an integrand. They might seem difficult but they are not. You can also try definite integral calculator and indefinite integral calculator with steps for solving definite integrand and indefinite integrand.

Derivative Calculator

The derivative calculator makes learning and solving differential equations convenient. It is an equation simplifier that employs the derivative quotient rule & its formula to calculate a function’s derivative. 

 The derivative calculator makes learning and solving differential equations convenient. It is an equation simplifier that employs the derivative quotient rule & its formula to calculate a function’s derivative. 

The derivative calculator is a great helping hand to practice calculus as it provides step by step differentiation. Moreover, if you don’t need to solve your whole problem using a derivative calculator, you can take reference of any step you are facing.

Thus, you can check your problem’s answer only or any step you need using an online derivative calculator.  Furthermore, the best thing about this tool is that there is no limit to how many you can differentiate your function. This tool allows you unlimited time to differentiate. 

Any function whether polynomial, exponential, rational, hyperbolic, irrational, logarithmic, trigonometric, or inverse hyperbolic could be performed and successfully solved using this derivative calculator. 


Integral Calculator

In relation to a given variable, it calculates an integral (antiderivative) of a function utilizing integration techniques. This calculator also enables the graphical representation along with their integral function. 

If you are curious and needs to how an integral calculator actually works? Then let us tell you the brief process, first of all, it parses the mathematical expressions, applies integration rules that are embedding inside it and provides the end result is a simpler manner. 

The ultimate result of the integral calculator could never be different from any other online tool. However, the procedure or steps taken might be different from that of other integral calculators.

You may incorporate any continuous function using the online integration calculator. To utilize this tool, input your functions and mention the variable you want to integrate along with the upper and lower limits of the function. To completely understand and correctly follow the procedure, consider the following syntax.

The general procedure for the use of the integral computer comprises:

  • The first step is to input the function in the fields provided as well as the lower and upper limit
  • Click the ‘Calculate’ option to receive the results of your integration step by step
  • The integral value will show in output along with all the steps followed beneath.

So here we learn about the online tools that we can use to solve complex integral and derivatives. There are a lot of modern learning techniques on Inspire spy which can enhance your advanced learning.