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anonymous
 one year ago
List x1, x2, x3, x4 where xi is the left endpoint of the four equal intervals used to estimate the area under the curve of f(x) between x = 4 and x = 6.
anonymous
 one year ago
List x1, x2, x3, x4 where xi is the left endpoint of the four equal intervals used to estimate the area under the curve of f(x) between x = 4 and x = 6.

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zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.1can you break this into \(4\) intervals \((4,6)\)?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I'm not understanding what it's looking for here..... @zzr0ck3r How would I do that? I don't recall anything like that.

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.1I think I will just show you, and then it will make sense \(x_1=4, x_2=4.5, x_3=5,\) and \(x_4=6\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So how did you choose those four numbers? I understand they are between 4 to 6 but is a random selection?

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.1it would be the only way to break the interval \([4,6]\) into \(4\) parts.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Don't think so https://gyazo.com/f25d718a61e95059646b790eba350188

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.1I meant \(x_4=5.5\) sorry

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.1want me to explain why?

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.1When we take the integral of something we are taking the area under the function, imagine you want to take the integral of the function \(f(x) = 2x+3\) from \(4\) to \(6\) The graph would look something like thisdw:1441154162616:dw

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.1we want the are under the graph from \(x=4, \) to \(x=6\). One way to approximate this area would be to break it up into four sections dw:1441154252671:dw Now we would estimate the area of each part We treat each part as a rectangle, so the area is 0.5 (the width of the rectangle) times \(f(4.5)\) . So the area of the first rectangle is estimated by \(0.5*f(4.5)\) and we get this area (approximately) dw:1441154442521:dw

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.1If we break this into infinite pieces, we would get the exact area, not just the approximate.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I understand why you did so...just how? Like why .5 and not .3?

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.1if I give you two dollars and ask you to break it into 4 even pieces, what would the size of each one be?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ok, that's why, the pieces must be even. So why wasn't the 6 included? Is it because it's the last and should already be known?
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