Integral calculus
What are Integrals?
The primitive value obtained after the integration is called the integral. The integrals are also called as antiderivative of the function.
What are the types of integrals?
There are two types of integrals:
- Definite Integrals
- Indefinite Integral
How to find the Integrals?
To evaluate we can use the integral calculus formulas, integration by substitution, integration by parts, integration by partial fraction.
Write some Applications of Integrals.
Some applications of integrals calculus are:
- To find the area of the curve
- To find the velocity from distance
- To find volumes of the solids
- To solve displacement and motion problems.
What is Definite Integral?
The antiderivative p(x) of the continuous function f(x) over the interval [a, b] is called definite integral. It is denoted by [Tex]\int\limits^b_a [/Tex]f(x) dx and equals to p(b) – p(a) where p(b) and p(a) are antiderivatives at x= b and x =a respectively.
How Do You Use Integrals using Trigonometry?
Use the trigonometric identities and simplify the function into integrable function and then apply the formulas and adopt the integration procedures to find the integrals using trigonometry.
Integral Calculus
Integral Calculus is the branch of calculus that deals with topics related to integration. Integrals are major components of calculus and are very useful in solving various problems based on real life. Some of such problems are the Basel problem, the problem of squaring the circle, the Gaussian integral, etc. Integral Calculus is directly related to differential calculus.
This article is a brief introduction to Integral Calculus, including topics such as fundamental theorems of integral calculus, types of integral, and integral calculus formulas, definite and indefinite integrals with their properties, applications of integral calculus, and their examples.
Table of Content
- What is Integral Calculus?
- Fundamental Theorems of Integral Calculus
- Integral Definition
- Types of Integrals
- Definite Integrals
- Definite Integral Formula
- Properties of Definite Integrals
- Indefinite Integrals
- Properties of Indefinite Integrals
- Improper Integrals
- Multiple Integrals
- Integral Calculus Formulas
- Methods to Find Integrals
- Applications of Integral Calculus
- Differential vs Integral Calculus
- Integral Calculus Examples
- Practice Problems on Integral Calculus
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