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anonymous
 one year ago
The function is continuous on the interval [10, 20] with some of its values given in the table above. Estimate the average value of the function with a Trapezoidal Sum Approximation, using the intervals between those given points.
x 10 12 15 19 20
f(x) –2 –5 –9 –12 –16
anonymous
 one year ago
The function is continuous on the interval [10, 20] with some of its values given in the table above. Estimate the average value of the function with a Trapezoidal Sum Approximation, using the intervals between those given points. x 10 12 15 19 20 f(x) –2 –5 –9 –12 –16

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jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1how far did you get?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Im stuck on how to start it

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0what trips me up is that it asks to use intervals between those values

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1I would start it by plotting the points on an xy grid (see attached)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0what would you do after plotting the points

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1then draw trapezoids

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1tell me what you get for the area of each trapezoid

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1dw:1443395568574:dw area of trapezoid = h*(B1+B2)/2 notice how the B1 and B2 are parallel

anonymous
 one year ago
Best ResponseYou've already chosen the best response.017.5 for the first trapezoid

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1yes for the one on the very left

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1now add up those areas to get ???

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0what would be the next step

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1dw:1443396060396:dw

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1imagine we have something like this function dw:1443396074151:dw some curve below the x axis

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1points A through E lie on this curve dw:1443396096733:dw

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1we can't get the exact area between the curve and x axis, but we can get the approximate area by using trapezoids dw:1443396136613:dw

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1it's not perfect, but it's the best we can do

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1what we do is divide the approximate area by the distance between the two endpoints (ba = 2010 = 10)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so the answer would be 8.4?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1you may have seen the formula \[\Large A = \frac{1}{ba}\int_{a}^{b}f(x)dx\] A = average value of the function f(x) on the interval x = a to x = b

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1so you just do 84/10 = 8.4

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1sorry yeah the area is actually negative because we're below the x axis 84/10 = 8.4

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0wow thank you so much! your explanation and steps were extremely helpful!

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1dw:1443396331117:dw
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