Table of Contents
Introduction to Integration
Integration is the process of combining two or more parts into a single whole. In mathematics, integration is the process of finding the area under a curve. Integration is a key concept in calculus, and is used to calculate the derivative of a function.
What is Integration in Maths?
Integration is a mathematical process that allows you to calculate the area of a curved shape. It is a way of finding the total length of a curve by breaking it down into a collection of straight lines.
In Mathematics, we Know That There are two Major Types of Calculus –
Differential calculus and Integral calculus.
Differential calculus is a branch of mathematics that deals with the rates at which quantities change. It is a method of finding the derivative of a function. The derivative is a measure of how a function changes with respect to a change in one of its inputs.
Integral calculus is a branch of mathematics that deals with the accumulation of quantities. It is a method of finding the integral of a function. The integral is a measure of the net change in a function over an interval.
What do you mean by Integral Calculus?
Integral calculus is a branch of mathematics that deals with the determination of the area under a curve, or more generally the accumulation of quantities.
Different Types of Integrals in Mathematics-
There are many different types of integrals in mathematics, but some of the more common ones include:
1. Riemann integrals
2. Lebesgue integrals
3. Improper integrals
4. Double integrals
5. Triple integrals
6. Surface integrals
7. Volume integrals
Types of Integration-
1. Partial integration-
This is the simplest form of integration and it is used to find the area of a simple shape. In this method, the area is divided into a number of small rectangles and the sum of the areas of these rectangles is calculated. This sum is then divided by the number of rectangles to find the average area per rectangle and the final answer is the sum of all the rectangle areas.
2. Standard integration-
This is the most basic form of integration and is used to find the area under a curve. In this method, the area is divided into a number of small intervals and the sum of the function values within each interval is calculated. This sum is then divided by the number of intervals to find the average function value within each interval and the final answer is the sum of all the interval function values.
3. Trapezoidal integration-
This is a more accurate form of integration and is used to find the area under a curve. In this method, the area is divided into a number of small trapezoids and the sum of the trapezoid heights is calculated. This sum is then divided by the number of trapezoids to find the average height of the trapezoids and the final answer is the sum of all the trapezoid heights.
What is a Definite Integral?
A definite integral is an integral in which the limits of integration are given.
Formulas of Integration
A. Integration by Parts
B. Integration by Substitution
C. Integration by Partial Fractions
D. Integration by Table
E. Integration by Trigonometric Substitution
