anonymous
  • anonymous
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
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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jim_thompson5910
  • jim_thompson5910
how far did you get?
anonymous
  • anonymous
Im stuck on how to start it
anonymous
  • anonymous
what trips me up is that it asks to use intervals between those values

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More answers

jim_thompson5910
  • jim_thompson5910
I would start it by plotting the points on an xy grid (see attached)
1 Attachment
anonymous
  • anonymous
what would you do after plotting the points
jim_thompson5910
  • jim_thompson5910
then draw trapezoids
1 Attachment
jim_thompson5910
  • jim_thompson5910
tell me what you get for the area of each trapezoid
jim_thompson5910
  • jim_thompson5910
|dw:1443395568574:dw| area of trapezoid = h*(B1+B2)/2 notice how the B1 and B2 are parallel
anonymous
  • anonymous
17.5 for the first trapezoid
jim_thompson5910
  • jim_thompson5910
incorrect
anonymous
  • anonymous
7
jim_thompson5910
  • jim_thompson5910
yes for the one on the very left
anonymous
  • anonymous
21 for the second
jim_thompson5910
  • jim_thompson5910
good
anonymous
  • anonymous
42 for the third
jim_thompson5910
  • jim_thompson5910
yep
anonymous
  • anonymous
and 14 for the last
jim_thompson5910
  • jim_thompson5910
very good
jim_thompson5910
  • jim_thompson5910
now add up those areas to get ???
anonymous
  • anonymous
84
anonymous
  • anonymous
what would be the next step
jim_thompson5910
  • jim_thompson5910
|dw:1443396060396:dw|
jim_thompson5910
  • jim_thompson5910
imagine we have something like this function |dw:1443396074151:dw| some curve below the x axis
jim_thompson5910
  • jim_thompson5910
points A through E lie on this curve |dw:1443396096733:dw|
jim_thompson5910
  • jim_thompson5910
we 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
  • jim_thompson5910
it's not perfect, but it's the best we can do
jim_thompson5910
  • jim_thompson5910
what we do is divide the approximate area by the distance between the two endpoints (b-a = 20-10 = 10)
anonymous
  • anonymous
so the answer would be -8.4?
jim_thompson5910
  • jim_thompson5910
you may have seen the formula \[\Large A = \frac{1}{b-a}\int_{a}^{b}f(x)dx\] A = average value of the function f(x) on the interval x = a to x = b
jim_thompson5910
  • jim_thompson5910
so you just do 84/10 = 8.4
jim_thompson5910
  • jim_thompson5910
sorry yeah the area is actually negative because we're below the x axis -84/10 = -8.4
anonymous
  • anonymous
wow thank you so much! your explanation and steps were extremely helpful!
jim_thompson5910
  • jim_thompson5910
|dw:1443396331117:dw|
jim_thompson5910
  • jim_thompson5910
no problem

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