Geometrical Interpretation of Integrals
Integrals are usually used for calculating the areas under the curve. Although there are formulas available, they are only available for standard shapes.
Often arbitrarily complex shapes are encountered, and it is not possible to develop and remember a formula for every shape. Thus, integrals help in generalizing the method for calculating the areas and the volume. Consider a function f(x), the objective is to calculate the area of the function.
The function is divided up into different parts in the shape of rectangles, these parts add up and form the area. The width of each rectangle is[Tex] \Delta x [/Tex]
As the number of rectangles increase, the width of these rectangles becomes very small and can be denoted by “dx”. The area of each rectangle becomes f(x)dx. The total area is the sum of areas of all these small rectangles,
A(x) = Σ(x) = ∫ f(x) dx
This is explained in the image added below:
Integrals
Integrals: An integral in mathematics is a continuous analog of a sum that is used to determine areas, volumes, and their generalizations. Performing integration is the process of computing an integral and is one of the two basic concepts of calculus.
Integral in Calculus is the branch of Mathematics that deals with finding integrals of the given functions. The branch of calculus that deals with integral is called Integral Calculus.
In this article, we will learn about the Integral definition, types, formulas, properties, examples solved problems, etc.
Table of Content
- What are Integrals?
- Integrals Definition
- Integrals Definition
- Types of Integrals
- Indefinite Integrals
- Definite Integrals
- Improper Integrals
- Integrals as Inverse of Differentiation
- Properties of Integrals
- Geometrical Interpretation of Integrals
- Integral Formulas
- Integrals Class 12
- Solved Questions on Integrals
- Integrals Practice Questions
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