Question

Express the integral as a limit of Riemann sums using right endpoints. Do not evaluate the limit. ??? ?(5 + x²) dx lim (n??) ?(i=1 to n) ( )

          Express the integral as a limit of Riemann sums using right endpoints. Do not evaluate the limit.

??? ?(5 + x²) dx

lim (n??) ?(i=1 to n) (      )

Express the integral as a limit of Riemann sums using right endpoints. Do not evaluate the limit.

??? ?(5 + x²) dx

lim (n??) ?(i=1 to n) ( )

Added by Daisy S.

Calculus Early Transcendentals

James Stewart 7th Edition

Chapter 5

Instant Answer

Solved by Expert Willis James

04/05/2021

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Transcript

0:00 Welcome to this lesson.

00:01 In this lesson, we write the area under the curve as a riemann sum using the summation sign.

00:16 So mostly we have the integral as the integral from a to b of a sudden function f of x, dx.

00:29 Under the remand sum, we find the we find a small change.

00:45 So if you have a few, so if you have to be here we divide this infinitely many times or probably many times and you find that each of these is the change in x or the small change that we have so that is given us the change in x that is given us b minus a all over n where n is the number of divisions that we have have so we go from b that is 5 to a that is 3 all over n and that gives us 2 over n okay so for each of this we have what is called the right word side of x at each bondage so that is x i and here we have a plus the change and when we come here we have 2a we have a again plus two times the change so it goes on and on and on until we come to the side where we have b or a plus and n times the change that results to b so here we see that we have a plus the change times i okay and this results to three plus two over n i for each of these right side of the boundary that we have all right then we can write the rimon sum as the limits as an approach is infinity of the sum from i from i equal to one to n of f the right word value for x for each of the divisions times the change in x okay so this so this is what we are looking for in a question so that becomes the limit as an approach is in functionality and now we have f of x already so in place of x we'll put 3 plus 2 we're having it as 5 plus x squared so in place of the x squared we'll put 3 plus 2 and i so that is squared then time times 3 or times 3 over n okay so here we have square root of 5 we can multiply this so we have two of this that makes it 3 over n i then plus 2 over n i times 3 over n i times 3 over n i and 2 over n okay so the whole thing again the limit as n approaches infinity this is 5 plus 9 plus 6 on n i then plus 6 on n i then plus 4 on n squared i squared still times 2 2 over n...

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