Question

An airplane's velocity is recorded at 5-min intervals during a 1-hour period with the following results, in miles per hour: 625; 640; 570; 580; 565; 550; 570; 600; 575; 595; 600; 575; 605; Use Simpson’s Rule to estimate the distance traveled during the hour. Answer in miles (using mi for miles) to the nearest whole mile.

Answer 1

Do you remember Simpson's rule?

Answer 2

It's a way to approximate integrals.

Answer 3

Yes, but I keep getting 588.056 miles, but I know that this is wrong. I can't tell what I messed up on.

Answer 4

I would suggest laying these out on a graph with a=550 to b=640; you then want to find the change in X of the interval:
\[\Delta x =\frac{b-a}n\]
Where n is the subintervals of equal length.

Essentially, you have something like this:
\[\int\limits_{550}^{640}f(x)dx= \frac{\Delta}3(f(x_0)+4f(x_1)+2f(x_2)+ \cdots + f(x_n))=S_n\]

Now just plug the values in to the formula and you should have the solution easily.

Answer 5

I'm guessing n=12?

Answer 6

If I take all of the repeats out, I get 10 data values, so n=10?

Answer 7

No. I erased the last comment because it was confusing. Sorry.

You should have n=12 and 12 x-values (they correspond). However, you have 13 values.