Consider the integral 5² (4x² + 3x + 4) dx 2 a) Find the Riemann sum using right end points and n=3 B3= b) Find the Riemann sum using left endpoints and n=3 L3=
Consider the integral 5² (4x² + 3x + 4) dx 2 a) Find the Riemann sum using right end points and n=3 B3= b) Find the Riemann sum using left endpoints and n=3 L3=
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![**Riemann Sums: An Introduction**
Consider the integral:
\[
\int_{2}^{5} (4x^2 + 3x + 4) \, dx
\]
**Part a: Right Endpoint Riemann Sum**
To find the Riemann sum using right endpoints and \( n = 3 \):
\[ R_3 = \]
**Part b: Left Endpoint Riemann Sum**
To find the Riemann sum using left endpoints and \( n = 3 \):
\[ L_3 = \]
In this exercise, you will practice calculating Riemann sums, which are methods for approximating the total area under a curve on a graph, otherwise known as the integral of a function.
For the right endpoint method, the interval is divided into \( n \) subintervals of equal length, and the function is evaluated at the right endpoint of each subinterval. Similarly, for the left endpoint method, the function is evaluated at the left endpoint of each subinterval.
Through these initial examples, you will grasp the fundamental concepts of numerical integration using Riemann sums.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffb2133c9-e1e5-4d56-9c72-044227328930%2Fb953ef51-6bed-4f10-91a7-8977d00ec533%2Fkvbeh2x_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Riemann Sums: An Introduction**
Consider the integral:
\[
\int_{2}^{5} (4x^2 + 3x + 4) \, dx
\]
**Part a: Right Endpoint Riemann Sum**
To find the Riemann sum using right endpoints and \( n = 3 \):
\[ R_3 = \]
**Part b: Left Endpoint Riemann Sum**
To find the Riemann sum using left endpoints and \( n = 3 \):
\[ L_3 = \]
In this exercise, you will practice calculating Riemann sums, which are methods for approximating the total area under a curve on a graph, otherwise known as the integral of a function.
For the right endpoint method, the interval is divided into \( n \) subintervals of equal length, and the function is evaluated at the right endpoint of each subinterval. Similarly, for the left endpoint method, the function is evaluated at the left endpoint of each subinterval.
Through these initial examples, you will grasp the fundamental concepts of numerical integration using Riemann sums.
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