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Approximating areas with a calculator Use a calculator and right Riemann sums to approximate the area of the region described. Present your calculations in a table showing the approximations for $n=10,30,60,$ and 80 subintervals. Comment on whether your approximations appear to approach a limit. The region bounded by the graph of $f(x)=\ln x$ and the $x$ -axis on the interval $[1, e]$

$$1.01$$

Calculus 1 / AB

Chapter 5

Integration

Section 1

Approximating Areas under Curves

Campbell University

Harvey Mudd College

Baylor University

Boston College

Lectures

03:09

In mathematics, precalculu…

31:55

In mathematics, a function…

04:10

Approximating areas with a…

04:41

03:58

05:39

05:15

02:37

Use a calculator and right…

02:51

03:14

02:16

02:59

Functions with absolute va…

Let's start by writing down what our X case star is. Well, since we're calculating the right hand some we want a plus. Okay, Delta X, A in this case is just one. And we want Delta X. No. So since we're working with 10 equals and equals 10 our daughter X is the distance in our domain. So it's e minus one, divided by the number petitions. We have 10 so that this will be our Dota X. So here we have e minus 1/10 times K. Now we can put that into our summation. I was a mission Goes from K equals 12 10 Whoops to 10 out and announced that of X will put our X K star. So we have Ellen of one plus E minus 1/10. Okay, All of this summed up and multiplied by Daughter X, which is e minus 1/10. Next, we have an equals 30. So our daughter X is e minus 1/30. So some equals k equals 12 30. Our function we keep the same. Except for now, don't exchanges to e minus 1/30 times K times The new Doctor X Next we have and equal 60. So our daughter X is e minus 1/60. So I was some equals. Summation from K equals 1 to 60 Ln one plus e minus 1 60 Okay, times e minus 1/60. These are the new daughter access. Lastly, we have and equals 80 Delta X equals e minus 1/80. So I was some equals summation from came, of course. 1 to 80 off l and one plus E minus 1/80 times K and everything multiplied by E minus 1/80. Now we're ready to put our summation table. Whoops. Everything keeps moving. Have n equals 10 30 60 and 80. And we have Awesome. So when you when you do the some the summations into your calculators, you should get one point Is your 84 1.28 1.14 And lastly, one point still 11 And as you can see, its end approaches to infinity. It gets closer and closer to this number. Here

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