Crystal K.

asked • 04/05/23

area and distance

The goal of this problem is to overestimate and underestimate the area under the graph of 𝑓(𝑥)=−20+12𝑥−𝑥2 from 𝑥=2 to 𝑥=10 using an “upper sum” and “lower sum” of areas of 44 rectangles of equal width.

the lower sum=48.

what would the upper sum=?

Patrick F.

tutor
Please double check that lower sum of 48. I get a lower sum of 402.38 Also, are you expected to calculate the areas of 44 rectangles for each sum, or can you use technology? If you know a little bit of python you can do this much faster.
Report

04/06/23

Joel L.

tutor
What I got for the 44 rectangles using Left Reimann Sum (lower sum) is about 85.289. That is still far from your answer. And the Right Reimann Sum (upper sum) is also about 85.289. There is a calculator for this in emathhelp (dot) net. Click Calculators and go to Calculus II. There you will see the Reimann Sum calculator both for left and right. Actually, if x=2 to 10, 44 rectangles are really thin and can possibly very close to the integral (approx. 85 1/3), which you can calculate in Desmos.
Report

04/06/23

Patrick F.

tutor
I missed the negative sign in front of the 20, and so my number is wrong. Joel, I don't think what is meant by the "upper sum" is the Right Reimann Sum. The "upper sum" should be the Right Reimann Sum for the increasing part of the function [2,6] and the Left Reimann Sum for the decreasing part of the function [6,10]. Vice versa for the "lower sum". I will post an illustration.
Report

04/06/23

Joel L.

tutor
For sure it's not more than 400.
Report

04/06/23

Patrick F.

tutor
Of course
Report

04/06/23

Crystal K.

Hello, yes the Lowe sum is 48! my professor and I did it together however, I just dont know the upper sum!
Report

04/07/23

1 Expert Answer

By:

Patrick F. answered • 04/06/23

Tutor
5 (14)

Inspiring Math Teacher with 20+ years of experience
About this tutor ›
About this tutor ›


Upvote • 0 Downvote
More
Report

Joel L.

tutor
A quote from calcworkshop.com "We will learn the notation and formulas for finding the Right and Left Rieman Sums (also known as the upper and lower sums), as well as the Midpoint Rule and the Trapezoidal Rule." But you made a great point.
Report

04/06/23

Still looking for help? Get the right answer, fast.

Ask a question for free

Get a free answer to a quick problem.
Most questions answered within 4 hours.

OR

Find an Online Tutor Now

Choose an expert and meet online. No packages or subscriptions, pay only for the time you need.