anonymous
  • anonymous
trapezoidal rule for uneven lengths?
Mathematics
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anonymous
  • anonymous
trapezoidal rule for uneven lengths?
Mathematics
schrodinger
  • schrodinger
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anonymous
  • 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
  • anonymous
oh nvm
amistre64
  • amistre64
usually there is an equation to follow.... can you be more specific?

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anonymous
  • anonymous
nvm about the NVM. there is no equation. im just given a table with x and y values.
amistre64
  • 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
  • anonymous
so youre saying i need to add to trapezoid rules?
anonymous
  • anonymous
t = 0 1 3 4 7 8 9 L(t) = 120 156 176 126 150 80 0
anonymous
  • anonymous
i need to find L(2)
mathteacher1729
  • 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
  • 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
  • anonymous
and without L(2) i'm left with an expression.
anonymous
  • anonymous
as an answer
amistre64
  • amistre64
is there a pattern you can detect?
anonymous
  • anonymous
nope, its all random Y values
amistre64
  • 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
  • anonymous
i dont understand
anonymous
  • anonymous
the question wants me to start from the first 4 hours, and that starts at time 0 right?
amistre64
  • 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
  • amistre64
your not going to get an exact number any way, the trap areas will see to that :)
anonymous
  • anonymous
yeah .... hope this isnot on the AP test cause ima fail
amistre64
  • amistre64
i got no idea when the first four hours area, I dont have the problem :)
anonymous
  • anonymous
alright, well thx for helping!
amistre64
  • amistre64
sure thing, if you wanna post the entire problem, then I might be able to discern it better :)
anonymous
  • anonymous
ok lets do that
anonymous
  • 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
  • anonymous
sorry the L(t) is mssed up
anonymous
  • anonymous
wait nevermind is good
amistre64
  • 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
  • anonymous
oh wait, so i should take it for the WHOLE thing then divide by 3?
anonymous
  • anonymous
well it says the first 4 hours of sale. not the whole 0-9 hours
anonymous
  • 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
  • amistre64
like this....
1 Attachment
anonymous
  • anonymous
yeah
amistre64
  • 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
  • anonymous
but the graph could have a decrease at 2 so it would not give me the right y value
amistre64
  • 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
  • amistre64
the trap rule is the "best guess" method anyways, so it wont be exact regardless of what you do :)
anonymous
  • anonymous
mmm ok
amistre64
  • amistre64
plot the points. connect the dots, take it where it leads you :)
anonymous
  • anonymous
ok thx

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