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Problem 38 Medium Difficulty

Shown is the graph of traffic on an Internet Service provider's T1 data line from midnight to 8:00 am. $ D $ is the data throughput, measured in megabits per second. Use Simpson's Rule to estimate the total amount of data transmitted during that time period.


$\approx 15696$ Mbits $\quad$

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Video Transcript

Okay. This question wants us to estimate the integral of this data graph using Simpsons Rule. So remember, Simpsons Roll says that the integral from A to B of F of X is approximately equal to the Simpson approximation, which is Delta X over three times f of a plus four times the odd sub intervals plus two times the even sub intervals plus effort be So now we just need to decide what our Ennis. So since the graph goes from zero to a and we like to pick imagers because it is easy to read, will have nine data points. And if we have nine data points, that means that end should be eight, cause we always pick data points minus one for n value. So that means that Delta X equals well, going from zero to a, and we have eight sub intervals. So Delta X is one which works out nicely. So from there, we can say that are integral is approximately equal to Subait, which is just 1/3 times F zero plus four times f of one plus two times f of two. Plus that that and this continues up until four times after seven plus f of age, and this will vary a lot because this craft could be kind of hard to read. So I got an answer of about 15 700 megabits. And again, anything in the 15 1,016,000 range is a pretty good estimate, depending on how you rounded.