What is a Definite Integral?
The definition of Definite Integral is that it is the curve’s area under the definite integral’s limit. The definite integral is denoted by . Here, ‘a’ and ‘b’ are the limits of the integral. “a” is called the upper limit of the integral, and “b” is called the lower limit.
Definite Integral Definition
The image given below shows the representation of the Definite Integrals.
The definite integral can also be defined as the antiderivative of any function in the interval [a, b], and now for any function F(x) whose derivative is, f(x), then in the interval [a, b] its definite integral is defined as,
= F(b) – F(a)
Definite Integral | Definition, Formula & How to Calculate
A definite integral is an integral that calculates a fixed value for the area under a curve between two specified limits. The resulting value represents the sum of all infinitesimal quantities within these boundaries. i.e. if we integrate any function within a fixed interval it is called a Definite Integral. The starting point of the interval is the lower limit of the definite integral whereas the endpoint of the interval is the upper limit of the definite integral.
The definite integral is widely used in advanced mathematics or mechanics or others. It is used for calculating the area of irregular curves, and the volume of random shapes, and there are many other advantages.
In this article, we will learn about, Definite Integrals, formulas, applications, and others in detail.
Table of Content
- What is a Definite Integral?
- Definite Integral Definition
- Definite Integral Formula
- Evaluating Definite Integrals
- Definite Integral as Limit of a Sum
- Definite Integral and Fundamental Theorems of Calculus
- First Fundamental Theorem of Calculus
- Second Fundamental Theorem of Calculus
- Steps for Calculating Definite Integral
- Properties of Definite Integral
- Definite Integral by Parts
- Applications of Definite Integral
- Definite Integral Examples
- Definite Integral Practice Problems
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