Math Riemann Sum Formula More Videos The Riemann summation method is needed to calculate the approximation of area under curves. In the case of right and left methods, the approximation is performed using right or left endpoints for each subinterval respectively. There are minimum or maximum methods to give approximation with the help of smaller or larger endpoints for each of the subintervals. The values of Riemann sum could be given as the sub intervals from top to the bottom right. In mathematics, the Riemann sum is defined as the approximation of an integral by a finite sum. It was named after the German mathematician Riemann in 19^{th} century. The most common application of Riemann sum is considered in finding the areas of lines or graphs. It can also be used for calculating the length of curves and other approximations too. The Riemann sum is calculated by dividing a particular region into shapes like rectangle, trapezoid, parabola, or cubes etc. Now you have to calculate the area for each of the given shapes and add them together to find the end result. This approach is used to find the numerical approximation too in the case of a definite integral even if calculus does not make it easy to find a closed-form solution. [a,b] = Closed interval divided into ‘n’ sub intervals f(x) = continuous function on interval x_{i} = Point belonging to the interval [a,b] f(x_{i}) = Value of the function at at x = xi \[\large S_{n}=\sum_{n}^{i-1}\int (x_{i})(x_{i}-x_{i-1})\] Here, errors are generated when adding up the areas of the different shapes. When shapes get smaller than usual then the sum approaches to the Riemann integrals. The basic idea behind the concept is dividing the domain into partition or pieces and multiply the size of each piece by some value of function taken on that piece or sum of all these products. Related posts: Maths Formulas for Class 12 Maths Formulas For Class 11 List of Basic Maths Formulas for Class 5 to 12 Three Dimensional Geometry Maths Formulas for Class 12 Chapter 11 Linear Approximation Formula | Linear Interpolation & Regression Formula Three Dimensional Geometry Formulas for Class 11 Maths Chapter 12 Arithmetic Progressions Formulas for Class 10 Maths Chapter 5 Determinants Maths Formulas for Class 12 Chapter 4 Confidence Interval Formula with Problem Solution & Solved Example Straight lines Formulas for Class 11 Maths Chapter 10 Euler Maclaurin Formula with Problem Solution & Solved Example List of Maths Formulas for Class 10th CBSE Definite Integral Formula Probability Maths Formulas for Class 12 Chapter 13 What is Integration? List of Integration by Parts Formulas What is Remainder Theorem? Remainder Theorem Proof & Remainder Formula What is Calculus? List of Basic Calculus Formulas & Equations Double Time Formula – Problem Solution with Solved Example Difference of Squares Formula | Regression Sum of Squares Formula Sum of Arithmetic Sequence Formula | Arithmetic Recursive Related Topics: Up Next Definite Integral Formula Don't Miss What is (a-b)^3 Formula? a^3-b^3 Formula | (a-b)^2 | (a+b-c)^2 Continue Reading Latest Popular Guest Post12 hours ago Increasing Instagram Followers Guest Post1 day ago What is Marketing Automation? Marketing Automation Tools Guest Post3 days ago How Machine Learning Changed The Traditional Ways Of Developing A Mobile App. Guest Post4 days ago Why Email Marketing Is Important For Ecommerce Business? Difference Between1 week ago How to Compare Vagrant, Kubernetes, Mesos, and Docker? Learn1 week ago Square and Square Root Table of 1 to 100 | 100 Square Root Chart Learn1 week ago How Many Seconds in a Minutes, Hour, Day, Week, Month and Year? Learn1 week ago How Many Hours in a Day, Week, Month and Year or Leap Year? Difference Between1 week ago Difference Between Apache Spark and Apache Flink Guest Post4 weeks ago Top 12 Big Data Certifications in Demand For 2020 Math8 months ago Average Rate Of Change Formula Made Simple Math8 months ago List of Basic Maths Formulas for Class 5 to 12 Math2 years ago Percentage Formulas | How to Calculate Percentages of a Number? Math2 years ago Surface Area of a Triangular Prism Formula & Volume of a Triangular Math2 years ago Triangular Pyramid Formula | Volume & Surface Area of a Triangular Pyramid Math2 years ago Y Intercept & X Intercept Formula | Slope Intercept Form & Equation Math2 years ago What is Integration? List of Integration by Parts Formulas Math8 months ago List of Basic Algebra Formulas for Class 5 to 12 Math2 years ago What is (a-b)^3 Formula? a^3-b^3 Formula | (a-b)^2 | (a+b-c)^2 Math2 years ago List of Pyramid Formula – Surface Area, Volume of Pyramid Advertisement