Table of Contents
Explain in Detail :Categories of Integration Calculus
There are three main categories of integration calculus: definite integrals, indefinite integrals, and the Fundamental Theorem of Calculus.
Definite integrals involve finding the area under a curve on a given interval. Indefinite integrals involve finding the integral of a given function, but do not specify an interval. The Fundamental Theorem of Calculus relates the definite and indefinite integrals, and shows that the area under a curve is the same as the integral of the function over the interval.
Definite Integral
The definite integral of a function is the limit, as the number of partitions goes to infinity, of the sum of the products of the function values and the lengths of the partitions.
The definite integral of a function can also be computed by using the Fundamental Theorem of Calculus.
Indefinite Integral
An indefinite integral is an integral in which the limits of integration are not specified.
The Uses of Integral Calculus
Integral calculus is a powerful tool for solving problems in physics and engineering. It can be used to find the volume or surface area of a three-dimensional object, or to calculate the speed and position of an object over time. Additionally, integral calculus can be used to find the most efficient path between two points or to optimize a system’s performance.
Integration Calculus Examples
The following are integration calculus examples:
1) Integrate x2 from 0 to 3.
The integral of x2 is x3/3.
2) Integrate x3 from 0 to 1.
The integral of x3 is x4/4.
