Riemann Sum
Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus.
Riemann Integral
Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.
Calculate the area under y = x^2
for 0 ≤ x ≤ 4 using a Riemann sum with n = 8 and left endpoints
Width of each subinterval = (4-0)/8= 4/8 = 0.5
So the partitions are 0, 0.5 , 1 , 1.5 , 2 , 2.5 , 3 , 3.5 , 4
For the left Riemann sum we will take the left endpoints, that is: 0, 0.5 , 1 , 1.5 , 2 , 2.5 , 3 , 3.5
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