The Function F is Continuous on the Closed Interval 0 6 and Has the Values Given in the Table Above
Get the answer to your homework problem.
Try Numerade free for 7 days
The function f continuous on the closed interval [0, 6] and has values as shown in the table above: What is the approximation of f(ldr obtained from using: A midpoint Riemann sum using the intervals [0,2] , [2,4], and [4,6]7 A Right Riemann sum using the intervals (0,2], [2,4]. and [4,61? A Left Riemann sum using the intervals [0,2], [2,4] and [4,6]? Right Riemann sum using the intervals (0,1], [1,2]. (2,31. [3,4L. [4 5L and [5,6]? Intervals [0,1], (4,2], (231 [341 [9Sulendleep
Related Question
The functions f is continuous on the closed interval [1 13] and bas values as shown in the table below. Using the subintervals [1,4] [4, 9,and [9,13], what is the approximation of jrc)dx found by using a right Riemann sum? f() 26 35 213 296 321 330
Discussion
You must be signed in to discuss.
Video Transcript
you know, evaluate this integral of F for fix dx from X equal to 1 to 13. And we see that this is approximately equal to the area Under the Girl of the four Fix. Under the code of a four effects from X equal to one. two x equals 30. So how do you find this area under the curve of the form X? Uh that is, we have to calculate the area under the curve of the four fix from Mexico to 1 to 13 for this. We are given that three sub intervals. So we are going to use this three sub intervals for each of the sub intervals. We're going to calculate the area of the rectangle within that interval sub interval and add them up together. So let's see how to do it. And went to consider the first sub interval that is 1:04. And we know that the area of a rectangle is with the times height. This is the general formula to find the area of a rectangle. With times you see that this is height was not a length. And so let's calculate the width of this red candle defined within this sub interval. The width is the X two minus X one. The difference between the X coordinates. So here it is four minus one and this equal street. So we say that the width of this rectangle is three. And to determine the height, we helped evaluate the function value At the right end point. So here food is the right endpoint. So we say that to the height of this rectangle is a 44. We can find a 44 from the table. Let's look at the table, we see that it is sounding so therefore the area of this rectangle equals, this is three times of a 44 is 17. Let's calculate this. This equals I plug it into the calculator, this is 51. So we found the area of the rectangle for the first to serve interval one comma four. So likewise, we have to find the area of the rectangle for the other two sub intervals. Let's do that. Now I'm going to consider the second sub interval that is four Kemal nine. And here I had to calculate the width and the height, The width is the difference in the X coordinates. So we say that it is 9 -4 and this equals five. So we put five here times the height is so we have to consider the right endpoint. So it is a four of nine And this equals five times four of nine is we can see from the table, it is 26. So we plug in 26 years And this kills 26 times five. This equals 130. Now let's calculate for the last sub interval that is 9-13. So here the witness 13 -9 and this equal sport and then we have to consider a 430 which is the height of the rectangle. So we consider the right endpoint for 13 from the table. It is 35. So let's plug in 35 here. So therefore this becomes four times of 35 and this equals 140. Now we have to add the areas of all the rectangles which we form using the three sub intervals. So it's basically 51 plus 130 Plus 140. Let me add it up Plus 51. So I get 321. This is the ideal under the curl of a for fix. This is the area under the go off. Mm hmm. If all fixed From x equals 1, 2 x equals 30. So therefore we see that there's different integral from 1-13. Therefore effects Bx. This is approximately equal to 300 and 21. And so we choose the option seat. That's correct.
Source: https://www.numerade.com/ask/question/the-function-f-continuous-on-the-closed-interval-0-6-and-has-values-as-shown-in-the-table-above-what-is-the-approximation-of-fldr-obtained-from-using-a-midpoint-riemann-sum-using-the-interva-88669/
0 Response to "The Function F is Continuous on the Closed Interval 0 6 and Has the Values Given in the Table Above"
Post a Comment