Question

trapezoidal rule for uneven lengths?

Answer 1

how can i take the trapezoidal rule estimation for X's that are not the same in difference? for example: i have x and y values for 0,1, and 3, but not 2. how do i find the y value of 2?

Answer 2

oh nvm

Answer 3

usually there is an equation to follow.... can you be more specific?

Answer 4

nvm about the NVM. there is no equation. im just given a table with x and y values.

Answer 5

then for the trap rule, I would assume the best you can do is add up all the individual areas that they give you right?

Answer 6

so youre saying i need to add to trapezoid rules?

Answer 7

t = 0 1 3 4 7 8 9
L(t) = 120 156 176 126 150 80 0

Answer 8

i need to find L(2)

Answer 9

Oh, so you're not even integrating, you're just trying to find what the function is when you evaluate it at a point which is not given. :)

Answer 10

well for now yes, but i need to use the trapezoid sum rule to find the approximate area. thats what my problem says

Answer 11

and without L(2) i'm left with an expression.

Answer 12

as an answer

Answer 13

is there a pattern you can detect?

Answer 14

nope, its all random Y values

Answer 15

if you cant determine L(2), then assume that the interval [1,3] is the base, and use the [L(1)+L(3)]/2 is the height

Answer 16

i dont understand

Answer 17

the question wants me to start from the first 4 hours, and that starts at time 0 right?

Answer 18

the area of a trapezoid is the base times the average height. i would just calculate the area between 1 and 3 and add it into the rest of it

Answer 19

your not going to get an exact number any way, the trap areas will see to that :)

Answer 20

yeah .... hope this isnot on the AP test cause ima fail

Answer 21

i got no idea when the first four hours area, I dont have the problem :)

Answer 22

alright, well thx for helping!

Answer 23

sure thing, if you wanna post the entire problem, then I might be able to discern it better :)

Answer 24

ok lets do that

Answer 25

Concert tickets went on sale at noon (t=0) and were sold out within 9 hours. the number of people in line waiting to buy tickets at time t is modeled by a twice differentiable function L for 0<=t <= 9.

Use a trapezoial sum rule with 3 sub intervals to estimate the average number of people waiting in line during the first 4 hours that tickets were on sale.

t = 0 1 3 4 7 8 9 L(t) = 120 156 176 126 150 80 0

Answer 26

sorry the L(t) is mssed up

Answer 27

wait nevermind is good

Answer 28

for starters, take the interval [0,9] and subdivide it into 3 equal intervals [0,3] ;[3,6] ;[6,9] is what it wants you to do right?

then you find the area for each trap made according to the value of the "endpoints" of each subinterval..

Answer 29

oh wait, so i should take it for the WHOLE thing then divide by 3?

Answer 30

well it says the first 4 hours of sale. not the whole 0-9 hours

Answer 31

i was thinking it strts at time 0 and ends at time 3 so that gives me 4 hours since people start to get tickets at time 0

Answer 32

like this....

Answer 33

yeah

Answer 34

..... yeah the first 4 hours. if anything plot all your points on a graph and connect the dots... then determine the heights of your intervals from that

Answer 35

but the graph could have a decrease at 2 so it would not give me the right y value

Answer 36

you cant get the "exact value" regardless, you just have to do the best with what you have.... you cant "create" data that doesnt exist..

Answer 37

the trap rule is the "best guess" method anyways, so it wont be exact regardless of what you do :)

Answer 38

mmm ok

Answer 39

plot the points. connect the dots, take it where it leads you :)

Answer 40

ok thx