Problem

Explain why or why not Determine whether the foll…

02:17

Problem 58 Easy Difficulty

Use a calculator and right Riemann sums to approximate the area of the given region.
Present your calculations in a table showing the approximations for $n=10,30,60,$ and 80 subintervals. Make a conjecture about the limit of Riemann sums as $n \rightarrow \infty.$
The region bounded by the graph of $f(x)=\left(2^{x}+2^{-x}\right)$ In 2 and the $x$ -axis on the interval [-2,2].

Answer

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Calculus 1 / AB

Calculus 2 / BC

Calculus Early Transcendentals

Chapter 5

Integration

Section 1

Approximating Areas under Curves

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Video Transcript

Okay, quick. Google search for Dez. Most re Mont sums. Um, in the first option, I think will even give you this. And you could just type in the function that they give you to the X Plus two thing And the wrecks. They want the balance from negative to now to the upper round of two. I still have an equals 10 saved from a previous video, And, uh, what we want still is a right three months. Um, so double check that this as Sequels One, um, I'm just re reading to make sure that we want the right Raymond solemn. And when we have 10 rectangles, we get an approximate answer of 10.889 which might be pretty good answer tryingto fit it all in. But zoom in enough that you can see that there's some white space here. So to the left is an under approximation. To the right is an over approximation. Eso This might not be the best answer. Um, sorry. Moving all over the page. And then we can change that. The 30 erecting a better approximation. And we get 10.828 Okay, well, maybe I'm not convinced yet s to switch over to 60. It's about 10.822 That right? Um okay, well, maybe we could get a better answer, like maybe put in and eight for 80 rectangles are getting slightly better is a 10.8 to 1. I don't even know if that's enough to really convince me what the correct answer is. Eso what's nice about an Internet based programs? It doesn't take long to think like I could do 800 rectangles, you know, 8000 rectangles, and the more zeros I put in here, I get better answers. And if you notice the difference between that last zero and the new one is the decimal doesn't actually change it all. Um, now, if I were a betting person, I feel like this number has something to do with, um to to a certain power, but I haven't actually calculated it yet, but 10.820 is probably a really, really good guess if your teacher accepts decimals for an answer, um, for the infinite limit. So the more erecting was that You have the closer and closer you're going to get to 10.820

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