Definite Integral Formula

What is Integral Calculus?

The process of finding the function from its derivative is called anti-derivative which is also referred to as Integration. In this process, the result obtained after the integration is called the integral. This integral and integration hold many properties and the study of these properties in the branch of mathematics is called Integral Calculus. Various methods in Integral Calculus are used in many ways such as to find the areas and volumes, approximate solutions of equations, calculate complex interactions of physical objects in our surroundings, etc....

Fundamental Theorems of Integral Calculus

The integral represents the area under the curve. There are two fundamental theorems of integral calculus:...

Integral Definition

The antiderivative of the function f is called the integral of f. The reverse of differentiation is called as integration. The integral is also called as the primitive function of f or Newton-Leibnitz integral. The integral is the area under the curve. There are two types of integral: Definite integral and indefinite integral....

Types of Integrals

Integrals can be classified as:...

Definite Integrals

The definite integrals are the integrals which are bounded by the limits. The antiderivative p(x) of a continuous function f(x) on the interval [a, b] is called a definite integral. It is denoted by [Tex]\int\limits^b_a  [/Tex]f(x)dx and its value equals to p(b) – p(a) where p(b) is the antiderivative at x = b and p(a) is the antiderivative at x = a. The interval [a, b] is called interval of integration. The a and b are called the limits of integration where a is called the lower limit and b is called the upper limit of the integration. The definite integral does not require any constant integration....

Definite Integral Formula

To calculate the definite integral of any function, we can use the Second Fundamental Theorem of Integral Calculus, which is already discussed above. According to that, the formula for Definite Integral is:...

Properties of Definite Integrals

Some properties of definite integrals are:...

Indefinite Integrals

The integrals that do not have the limit of integration are called indefinite integrals. The indefinite integrals involve the addition of constant of integration. The integration of the function f(x) is represented by F(x) and is given by...

Properties of Indefinite Integrals

There are several properties of integral calculus:...

Improper Integrals

The integrals whose integrand is not bounded, or the limit of the integral is infinity, then the integral is called as improper integrals. Some examples of improper integrals are: [Tex]\int\limits_1^\infty  [/Tex]f(x)dx or [Tex]\int\limits^1_0  [/Tex][dx/x]...

Multiple Integrals

Multiple integrals are integrals with more than one variable. There are two types of multiple integrals. They are:...

Integral Calculus Formulas

Integral calculus formulas are as follows:...

Methods to Find Integrals

There are multiple types of integrals which can be solved using different methods. Some integrals can be directly solved by applying formulas. To solve some integrals, we use the following methods:...

Applications of Integral Calculus

Integral calculus has different applications. Some of them are:...

Differential vs Integral Calculus

The key differences between Differential calculus and Integral calculus are listed in the following table....

Integral Calculus Examples

Example 1: Solve: ∫x9dx...

Practice Problems on Integral Calculus

1. Calculate the integral of the function: ∫(3x2 – 5x + 4) dx...

FAQs on Integral calculus

What are Integrals?...