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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 $f(x)=12-3 x^{2}$ and the $x$ -axis on the interval [-1,1].
n Right Riemann sum10 21.9630 21.995660 21.998980 21.9994
Calculus 1 / AB
Calculus 2 / BC
Chapter 5
Integration
Section 1
Approximating Areas under Curves
Integrals
Integration Techniques
Oregon State University
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all right. So it is washing. We are asked to take the ravings. Um, does make the area amusing, increasing, um, values for the number of sub intervals. And so I've got users written note in table. That's a question. As for a year for any was 10 of everyone's on 21.9 600 then all the way up to one in 80 our end is 21.994 So the way to do this question is you got your first tightly the length of the Southern Wall using before Delta X equals B minus a over and or Beamon's A is the range. Next, you calculate the endpoints of each sub in a role. Using the Formula X K was a plus, Kate out the hex, and then you're gonna take the some of f of x k times. Don't x from a K one to k equals n the number of seven rules. Um, and so what you're doing there is you're plugging in your expression for XK into the expression for the function, and then you're summing it up, using you for their and that is how you will get value in the table over here. It could be asked us a vote. What? It means that, um, what increasing number of sub animals means. Um so as an approaches infinity, the area purchase the estimate for the area under a curve approaches the approaches, the exact area. And we can see that as we increase end Looking at the table, we are approaching 22 s o. It would appear that the exact area under the curves would be 22.
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