Definite Integral Examples
Example 1: Find the Integral:
Solution:
Solving,
Example 2: Evaluate
Solution:
2log2-2+1=(2log2-1)
Example 3: Integrate
Solution:
Applying G.P, a=1. r=e2/n, we will get,
Using,
Example 4: Evaluate
Solution:
a=-1, b=2, f(x)=5x
h=(b-a)/n=3/n, nh=3
By definition:
Example 5: Evaluate,
Solution:
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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