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How To Do Integration? | Fundamentals of Calculus

Home > Creations > How To Do Integration? | Fundamentals of Calculus

Akarshit MahajanLast Seen: Dec 6, 2023 @ 9:58am 9DecUTC
Akarshit Mahajan

Integration is the heart of calculus without which the subject of calculus is soulless. Even you can not master any advanced mathematical skill if you are weak at integration simplification. 

But do not worry! In this research-based article, we will be exploring ways to resolve integrals. A few will be manual and the other will be using an integral calculator. 

Exploring a little more integration calculator, this online tool is a boss in calculating integration answers without a delay. By using it, you get complete steps involved in the integration procedure. 


A mathematical technique that helps you to find area, volume, and central points lying under a certain graph. 

Types of Integrations:

The following are the two basic types of integrals that you must master. These can also be simplified by an integral calculator in seconds. 

Definite Integral

It represents the area under the curve.

abf(x) dx

Indefinite Integral:

This kind of integration is defined without using any lower and upper limits. 

f(x) dx

Basic Integration Formulas:

To master integration, you need to remember the following basic integration formulas:

1 dx = x + C

a dx = ax + C

x” dx = n+1 + C; n  is not equal to 1

sin x dx= -cos x + C

cos x dx = sin x + C

sec2 x dx = tan x + C

csc2 x dx = – cot x + C

sec x(tan x) dx = secx+ C

fcsc x(cot x) dx = cscx + C

dx = In |x|+C

Product Rule of Integration:

The rule of integration for products of two functions is known as the product rule. It is the integration equivalent to the differentiation’s “product rule.” The following is an explanation of the product rule of integration:

∫(u * v) dx = u ∫v dx – ∫(u’ ∫v dx) dx

The integral calculator also uses the same default expression to find the product of two functions with 100% accuracy.

Following these steps will help you apply the product rule of integration:

  • Identify the integral’s u and v

  • Find u by differentiating u

  • To determine v dx, integrate v

  • the product rule formula using the values acquired in stages 2 and 3

  • If you can, make the phrase simpler

Use Online Integral Solver:

The tool is another gem in resolving integration related issues in no time. Students and professional mathematicians around the globe use this advanced calculator to resolve their integral queries without any delay. 

Using this integral calculator is so simple as it requires you to follow these steps to get your results:

  • Open the tool 

  • Select the type of integral

  • If it is indefinite, simply enter your function in its field

  • If it is a definite integral, set lower and upper bounds as well

  • Once done, hit the calculate button and the integration calculator will instantly display all steps involved in results


What purpose does integration serve?

Numerous items can have their volume, area, and central values determined via integration.

What are some examples of integration in practice?

Integrations are crucial for calculating the gravitational and mass centers as well as for predicting the positions of the planets and other astronomical objects.

What is the calculus fundamental theorem?

The calculus fundamental theorem connects the ideas of function differentiation and integration.

 Things To Conclude

  • Learn mathematics by heart

  • Understand how to apply integration formulas

  • Learn how to use the advanced integral calculator for free

  • Remember various techniques of integration for examinations

Akarshit MahajanLast Seen: Dec 6, 2023 @ 9:58am 9DecUTC

Akarshit Mahajan


Published: | Last Updated: | Views: 35

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