Difference Between Lebesgue Integral and Riemann Integral
The difference between Lebesgue integral and Riemann integral can be understood from the table below:
Lebesgue Integral | Riemann Integral |
|---|---|
Subdivides the y-axis to measure the inverse image of sets and adds them up. | Subdivides the x-axis into intervals and adds up the surface area of rectangles. |
Allows for a countable infinity of discontinuities, making it more flexible in handling complex functions. | Only permits a finite number of discontinuities, which may limit its ability to handle certain functions with a higher degree of irregularity. |
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Riemann Integral
Riemann integral is a method used in calculus to find the area under a curve, or the total accumulated quantity represented by the curve, between two specified points. In this article, we will understand the Riemann sums, formula of Riemann integral, properties of Riemann integral and applications of Riemann integral. At the end of this article, we have given solved and practice questions for better understanding.
Table of Content
- What is Riemann Integral?
- Riemann Sums
- Riemann Integral Formula
- Properties of Riemann Integral
- Applications of Riemann Integral
- Examples of Riemann Integral