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.
We can calculate the Riemann sum for em with six subintervals and taking the sample points as the left ends. This situation is represented in the figure 8.1. Taking into account the formed rectangles, we can say that the function of image 8.2 is:
| A) |
-5 |
| B) |
5 |
| C) |
6 |
| D) |
4 |
| E) |
-6 |
Given that,
n = 6
From the integral we have a = 2, b = 14.
The formula to find left Riemann sum is,
Where the points 
are the left endpoints of the subinterval.
Now find the 6 subintervals of length 
between the interval [ 2, 14].
Subintervals: [2, 4], [4, 6], [6, 8], [8,10], [10, 12], [12, 14].
The left endpoint of the interval [2, 4] is 2.
The left endpoint of the interval [4, 6] is 4.
The left endpoint of the interval [6, 8] is 6.
The left endpoint of the interval [8, 10] is 8.
The left endpoint of the interval [10, 12] is 10.
The left endpoint of the interval [12, 14] is 12.
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