A car is entering the highway, and accelerates in the first 30 seconds, as follows: time (in seconds) 6 12 18 24 30 speed (in meters per second) 2 10 16 20 23 25 Use a Riemann sum, with 5 equal subintervals, to underestimate the distance travelled by the car over these 30 seconds. Would you use left- or right-endpoints in your estimation? Explain.
A car is entering the highway, and accelerates in the first 30 seconds, as follows: time (in seconds) 6 12 18 24 30 speed (in meters per second) 2 10 16 20 23 25 Use a Riemann sum, with 5 equal subintervals, to underestimate the distance travelled by the car over these 30 seconds. Would you use left- or right-endpoints in your estimation? Explain.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.1: Infinite Sequences And Summation Notation
Problem 73E
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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
Transcribed Image Text:A car is entering the highway, and accelerates in the first 30 seconds, as follows:
time (in seconds)
12
18
24
30
speed (in meters per second)
10
16
20
23
25
Use a Riemann sum, with 5 equal subintervals, to underestimate the distance travelled by the car over these 30 seconds. Would you
use left- or right-endpoints in your estimation? Explain.
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