## 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

1. jim_thompson5910

how far did you get?

2. anonymous

Im stuck on how to start it

3. anonymous

what trips me up is that it asks to use intervals between those values

4. jim_thompson5910

I would start it by plotting the points on an xy grid (see attached)

5. anonymous

what would you do after plotting the points

6. jim_thompson5910

then draw trapezoids

7. jim_thompson5910

tell me what you get for the area of each trapezoid

8. jim_thompson5910

|dw:1443395568574:dw| area of trapezoid = h*(B1+B2)/2 notice how the B1 and B2 are parallel

9. anonymous

17.5 for the first trapezoid

10. jim_thompson5910

incorrect

11. anonymous

7

12. jim_thompson5910

yes for the one on the very left

13. anonymous

21 for the second

14. jim_thompson5910

good

15. anonymous

42 for the third

16. jim_thompson5910

yep

17. anonymous

and 14 for the last

18. jim_thompson5910

very good

19. jim_thompson5910

now add up those areas to get ???

20. anonymous

84

21. anonymous

what would be the next step

22. jim_thompson5910

|dw:1443396060396:dw|

23. jim_thompson5910

imagine we have something like this function |dw:1443396074151:dw| some curve below the x axis

24. jim_thompson5910

points A through E lie on this curve |dw:1443396096733:dw|

25. 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|

26. jim_thompson5910

it's not perfect, but it's the best we can do

27. jim_thompson5910

what we do is divide the approximate area by the distance between the two endpoints (b-a = 20-10 = 10)

28. anonymous

so the answer would be -8.4?

29. 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

30. jim_thompson5910

so you just do 84/10 = 8.4

31. jim_thompson5910

sorry yeah the area is actually negative because we're below the x axis -84/10 = -8.4

32. anonymous

wow thank you so much! your explanation and steps were extremely helpful!

33. jim_thompson5910

|dw:1443396331117:dw|

34. jim_thompson5910

no problem