Question

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

Answer 1

how far did you get?

Answer 2

Im stuck on how to start it

Answer 3

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

Answer 4

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

Answer 5

what would you do after plotting the points

Answer 6

then draw trapezoids

Answer 7

tell me what you get for the area of each trapezoid

Answer 8

area of trapezoid = h*(B1+B2)/2

notice how the B1 and B2 are parallel

Answer 9

17.5 for the first trapezoid

Answer 10

incorrect

Answer 11

7

Answer 12

yes for the one on the very left

Answer 13

21 for the second

Answer 14

good

Answer 15

42 for the third

Answer 16

yep

Answer 17

and 14 for the last

Answer 18

very good

Answer 19

now add up those areas to get ???

Answer 20

84

Answer 21

what would be the next step

Answer 22

imagine we have something like this function



some curve below the x axis

Answer 23

points A through E lie on this curve