trapezoidal rule for uneven lengths?

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- anonymous

trapezoidal rule for uneven lengths?

- schrodinger

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- anonymous

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?

- anonymous

oh nvm

- amistre64

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

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- anonymous

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

- amistre64

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?

- anonymous

so youre saying i need to add to trapezoid rules?

- anonymous

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

- anonymous

i need to find L(2)

- mathteacher1729

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. :)

- anonymous

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

- anonymous

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

- anonymous

as an answer

- amistre64

is there a pattern you can detect?

- anonymous

nope, its all random Y values

- amistre64

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

- anonymous

i dont understand

- anonymous

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

- amistre64

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

- amistre64

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

- anonymous

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

- amistre64

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

- anonymous

alright, well thx for helping!

- amistre64

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

- anonymous

ok lets do that

- anonymous

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

- anonymous

sorry the L(t) is mssed up

- anonymous

wait nevermind is good

- amistre64

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..

- anonymous

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

- anonymous

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

- anonymous

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

- amistre64

like this....

##### 1 Attachment

- anonymous

yeah

- amistre64

..... 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

- anonymous

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

- amistre64

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..

- amistre64

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

- anonymous

mmm ok

- amistre64

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

- anonymous

ok thx

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