Refer a friend and earn $50 when they subscribe to an annual planRefer Now

Get the answer to your homework problem.

Try Numerade Free for 30 Days

Like

Report

Find the sum of the areas of 10 circumscribed rectangles for each curve and show that the exact area (as shown in Exercises $15-18$ ) is between the sum of the areas of the circumscribed rectangles and the inscribed rectangles las found in Exercises $5(b)-8(b)$ ). Also, note that the mean of the two sums is close to the exact value.$y=2 x+1$ between $x=0$ and $x=2$ [compare with Exercises 6(b) and 16]. Why is the mean of the sums of the inscribed rectangles and circumscribed rectangles equal to the exact value?

Calculus 1 / AB

Chapter 25

Integration

Section 3

The Area Under a Curve

Integrals

Campbell University

Harvey Mudd College

Baylor University

University of Nottingham

Lectures

03:09

In mathematics, precalculu…

31:55

In mathematics, a function…

02:03

The area under a curve is …

06:35

In Exercises 17–20, comple…

01:57

Write and evaluate a sum t…

01:23

Approximate the area under…

01:15

a. Graph the curve $y=\fra…

02:49

In the following exercises…

03:07

03:18

01:49

06:43

Okay. So, uh, how to approach this problem? Let's start by drawing a curve here. Ah, so say the curve will look something like that. Ah, and maybe I'll dry twice. I'll drive. I'll draw the same cove again. Ah, so try to make it the same on Duh. So one of these, we were estimate using an inscribed rectangle. Remember? We're trying to estimate the area inside the coat on one of these will estimate using a circumscribe rectangle. Okay. Ah. As you can see, when we estimate using an inscribed rectangle we have Ah, we haven't underestimate on the stuff I shaded in black basically will be. The year will be an area. That Majesty error on here would have an underestimate. Okay, Um, so this is an open. We have an overestimate with this. Ah, with an error that's shaded in black over here, on the right on that. You can see one of these is in overestimate. At one of these is an underestimate. Ah, And if we take the mean of these two rectangular areas, we will we will cancel out some of the overestimate with the underestimate. And hence, this is why we shall expect to get a more accurate estimation of the true area and they need the code. Thanks for watching

View More Answers From This Book

Find Another Textbook

In mathematics, precalculus is the study of functions (as opposed to calculu…

In mathematics, a function (or map) f from a set X to a set Y is a rule whic…

The area under a curve is estimated using inscribed rectangles and circumscr…

In Exercises 17–20, complete the following.(a) Draw the graph of the fun…

Write and evaluate a sum to approximate the area under each curve for the do…

Approximate the area under the curve $f(x)=x^{2}$ for the interval $0 \leq x…

a. Graph the curve $y=\frac{1}{3} x^{3}$ .b. Use inscribed rectangles to…

In the following exercises, use a calculator to estimate the area under the …

Write and evaluate a sum to estimate the area under each curve for the domai…

92% of Numerade students report better grades.

Try Numerade Free for 30 Days. You can cancel at any time.

Annual

0.00/mo 0.00/mo

Billed annually at 0.00/yr after free trial

Monthly

0.00/mo

Billed monthly at 0.00/mo after free trial

Earn better grades with our study tools:

Textbooks

Video lessons matched directly to the problems in your textbooks.

Ask a Question

Can't find a question? Ask our 30,000+ educators for help.

Courses

Watch full-length courses, covering key principles and concepts.

AI Tutor

Receive weekly guidance from the world’s first A.I. Tutor, Ace.

30 day free trial, then pay 0.00/month

30 day free trial, then pay 0.00/year

You can cancel anytime

OR PAY WITH

Your subscription has started!

The number 2 is also the smallest & first prime number (since every other even number is divisible by two).

If you write pi (to the first two decimal places of 3.14) backwards, in big, block letters it actually reads "PIE".

Receive weekly guidance from the world's first A.I. Tutor, Ace.

Mount Everest weighs an estimated 357 trillion pounds

Snapshot a problem with the Numerade app, and we'll give you the video solution.

A cheetah can run up to 76 miles per hour, and can go from 0 to 60 miles per hour in less than three seconds.

Back in a jiffy? You'd better be fast! A "jiffy" is an actual length of time, equal to about 1/100th of a second.