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anonymous
 one year ago
Estimate the area under the curve f(x) = x^2 + 1 from x = 0 to x = 6 by using three circumscribed (over the curve) rectangles. Answer to the nearest integer.
anonymous
 one year ago
Estimate the area under the curve f(x) = x^2 + 1 from x = 0 to x = 6 by using three circumscribed (over the curve) rectangles. Answer to the nearest integer.

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So the interval would be from [0,2] [2,4] [4,6]?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0do you know which endpoints you're using?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Would the endpoints not be 1 to 6?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0you only have three intervals. I meant endpoints in terms of right or left of the interval

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0can you draw the rectangles? dw:1441160832388:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1441160946061:dw Something like this?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yes. so the width of all the rectangles will be 2. The heights will the yvalues at 2, 4, and 6. Make sense?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ok, so how would this help me setup my integral?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0This is the integral\[\int\limits_{0}^{6}(x^2+1) dx\] But that's not what you're being asked to find/evaluate. You're being asked for an estimate of the area, and you use the rectangle you drew to find it. For example, the area of the first rectangle is 2f(2) because 2 is its width and f(2) is its height. So you really just need to find the areas of the 3 rectangles and add them up

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[A=2f(2)+2f(4)+2f(6)\] \[A=2[f(2)+f(4)+f(6)]\] You have to plug in 2, 4, and 8 into \(f(x)=x^2+1\) to get f(2), f(4), and f(6) dw:1441161661208:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0sorry, typo. it's supposed to be 6
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