Question

I need to use Simpson's Rule to estimate the distance travelled by a cyclist. I've been given the instantaneous speed (v) in mph and the time in minutes for 10 one minute intervals. I don't know what my function should be to calculate the distance. Any help? Thanks!

Answer 1

\[\int\limits_{a}^{b} ydx= \frac{ h }{ 3 }[y0+4(y1+y3+y5+....)+2(y2+y4+y6+....)+yn]\]

Answer 2

where a to b is the interval
h is the difference between two intervals
y is the function itself
and yo to yn are the values of function at each interval
for e.g., if y=1+x
then y0= the value of y at x=0 which is 1 so y0=1

Answer 3

so here, h=1 because of 1 minute interval
and function y=distance =speed/time
y0 =value of y when x=0( x can be the variable you can adjust in speed/time)
y1= value of y at x=1 and so on

Answer 4

Thank you!
Yeah, I did have all that except the y. Did you explain how I actually figure out what my function is? I don't know the function for finding distance with given instantaneous speed.

Answer 5

distance =speed *time
you got instantaneous speed, you got time, your function is complete.

Answer 6

sorry., in above post i have written distance=speed/ time by mistaken

Answer 7

Thank you!!

Answer 8

you are welcome : )

Answer 9

@neer2809 One more question.: Do I need to change my data for my speed to miles per minute? My time is given in minutes and my speed in miles per hour.
:

Answer 10

yes you do

Answer 11

Great!! Thank you!!

Answer 12

do you know where simpsons rule is coming from

Answer 13

i remember doing it for my numerical methods class but its all kind hazy, i remember some other approximations to integration.. rhomberg or something simponds 1/3 and 3/8 stuff like that

Answer 14

It comes from using parabolas instead of straight line segments to approximate a curve.