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