The Riemann sums for a function f on the interval [1, 5] are given as E (2 - u)Ax, where [1. 5] is partitioned into n subintervals [x-1. ] of width Ar; and u, is some number in [x,-1, ]. If lim E (2 – u)Ax, exists, it man A0 (2-4)Ax, exists, it equals (B) (2-)Ax (A) (O 2-dr (D) 2-rt
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.
![2. The Riemann sums for a function f on the interval [1, 5]
are given as (2 - u) Ax, where [1, 5] is partitioned
into n subintervals [x-1, X] of width Ax; and u, is some
number in [x,-1, X]. If lim E (2- u) Ax, exists, it
max Ax-0=
equals
(A)
(B) (2- u) Ax
(O(2-rds
(D) 2-ds](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F06c6a2a6-7749-4f28-9cd9-9408371d2526%2F78fc48b3-e1c6-4c9b-8995-fd1086f18ad4%2F0vnescd_processed.jpeg&w=3840&q=75)
Here the given function is continuous and non-negative defined on the closed interval [1, 5]
The given interval divided into n subintervals defined as:
1 = x0 < x1 < x2 < … < xi < … < xn = 5
The n subintervals is defined as:
[1, x1] , [x1, x2], … , [xn-1, 5]
the above subdivision is called partition of the given interval.
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