Use the definition of the Riemann integral to show that f is Riemann integrable in [-1, 1] and compute the integral S f (x) dx.
Use the definition of the Riemann integral to show that f is Riemann integrable in [-1, 1] and compute the integral S f (x) dx.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter5: Rings, Integral Domains, And Fields
Section5.4: Ordered Integral Domains
Problem 5E: 5. Prove that the equation has no solution in an ordered integral domain.
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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.
Question
![3. Consider the function f : [-1, 1] → R given by
|1, x > 0,
f(x) =
x < 0.
Use the definition of the Riemann integral to show that f is Riemann integrable in [-1, 1] and compute
the integral , f (x) d.x.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9258a40d-e0f8-4871-9be6-cdef6325c2bc%2F45cc9803-b0c3-4def-8e51-880899f677ec%2Fq1c8yvu_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3. Consider the function f : [-1, 1] → R given by
|1, x > 0,
f(x) =
x < 0.
Use the definition of the Riemann integral to show that f is Riemann integrable in [-1, 1] and compute
the integral , f (x) d.x.
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