Question

The function f is continuous on the interval [2, 10] with some of its values given in the table below. Use a trapezoidal approximation with 4 trapezoids to approximate the integral from 2 to 10 of f of x dx.

Answer 1

https://gyazo.com/beafcad65c1c6321f2fc578f0f5b7583

Answer 2

@jim_thompson5910 Only person who seems to know calc

Answer 3

how far did you get?

Answer 4

Just started the problem.

Answer 5

I'm currently graphing online

Answer 6

Just decided that my graphing calculator would be a more efficient solution.

Answer 7

I agree. So you are able to plot the points and calculate the area of each trapezoid?

Answer 8

Plotted the points, kind of stuck on the trapezoid part.

Answer 9

What trapezoids are they referring to?

Answer 10

does this graph help at all (see attached) ?

Answer 11

here's a bigger version

Answer 12

Yes, the first one seems to be a triangle though

Answer 13

well if one parallel side of a trapezoid is 0, then we have a triangle

Answer 14

so you can either use the triangle area formula or the trapezoid area formula (with one base being 0)

Answer 15

Got 2.4 for the first one.

Answer 16

4.7 for the second one.

Answer 17

incorrect

Answer 18

Seriously?

Answer 19

yes

Answer 20

Damn calculator failed me, now I have to manually solve

Answer 21

maybe you typed in the wrong thing?

post what you typed in so I can see

Answer 22

I went to STAT and put in the table above X under L1 and Y under L2

Answer 23

I then went to STAT CALC and calculated a quadratic formula almost equal to the points in stat.

Answer 24

why not just compute the area of each trapezoid using

A = h*(b1+b2)/2

Answer 25

refer to my image attachment

http://assets.openstudy.com/updates/attachments/563abfcfe4b031eb5b29ec94-jim_thompson5910-1446692170541-graph3.png

Answer 26

Thought I could use a shortcut.

Answer 27

Which failed. So I'll do that now.

Answer 28

First 2*4*1/2 = 4
Second 3*(3+8)/2 = 33/2
Third 2*(8+15)/2 = 23
Fourth (15+17)/2 = 16

Answer 29

Total 59.5

Answer 30

Right?

Answer 31

`First 2*4*1/2 = 4` .... disagree; you have the wrong numbers
`Second 3*(3+8)/2 = 33/2` agree
`Third 2*(8+15)/2 = 23` agree
`Fourth (15+17)/2 = 16` disagree; should be 15 and 18 (not 15 and 17)

Answer 32

First 2*3*1/3= 3
Fourth (15+18)/2= 33/2

Answer 33

Final is 59.

Answer 34

`First 2*3*1/3= 3` agree
`Fourth (15+18)/2= 33/2` agree
`Final is 59.` agree

Answer 35

I have a similar one but it asks me to find f'(9) should I make a new post?

Answer 36

And as always, thanks.

Answer 37

`should I make a new post?` yes please