Question

can someone explain simpson's rule to me, im trying to plug this into my TI-83+ and having some issues.

Answer 1

\[\int\limits_{0}^{\pi}x^2sinx\] n=8
i know that the formula goes \[\frac{ \Delta x }{ 3 }\]and the coefficient pattern is: 1,4,2,4,2,4,1 but what about when going to 8?

Answer 2

Width of the intervals (which you divided) is: \[\Delta x = \frac{ b-a }{ n }\]. What makes Simpsons rule different from trapezoid/ midpoint is that you're dealing with quadratics.

Answer 3

For timesake, I'm not going to draw the graph, but you can do it on Wolfram or some computer program such as MatLab or Mathematica.

Answer 4

right o, i have that portion down but i don't know the coeffeciant pattern up to 8, i do know that i needs to be divisible by 2.
but then setting it up in my ti-83+ to get a table readout is one issue i haveing

Answer 5

Simpsons Rule:
\[\int\limits_{a}^{b}f(x)dx \approx \frac{ \Delta x }{ 3 }[f(x_0)+4f(x_1)+2f(x_2)+...+2f(x_{n-2})+4f(x_{n-1})+f(x_n)]\]

Answer 6

notice that all the function evaluations at points with ODD subscripts are multiplied by 4 n function evaluations at points with even subscripts (except for the first and last) are multiplied by 2. It might help you remember this rule if you note that.

Answer 7

right o that actually helps quite a bit! thank you @abb0t i will jot down that hint right now

Answer 8

Start by finding your width of ur subintervals, then the subinterval(s) and apply simpsons rule.

Answer 9

well the width of the intervals should be pi/8. correct?

Answer 10

since that is my deltaX

Answer 11

Yeah π/8

Answer 12

\[\Delta x = \frac{ b - a }{ n } = \frac{ \pi - 0 }{ 8 }\]

Answer 13

alright, now i am still confused since the prof only showed one example of setting up the table in the calculator, the table start is my endpoint or should i make that my first point then make it jump ("delta Tbl") by pi/8?

Answer 14

I've never been allowed to use calculator in any of my math courses so I really don't know what to input on the TI-83. I know statistics functions but that's about as far as I know.

Answer 15

instead of taking the time to calculate it out, we can use the table in the calc to help get the decimal values to plug into the equation and then solve. to save time

Answer 16

haha, thats alright. i know generally what i need to do i just am confused on what goes where in the setup...

Answer 17

i believe that i need to start at a, the endpoint, when setting up the table then have it jump by the deltaX - but either way thank you very much for the help and the coefficient pattern tip too, @abb0t

Answer 18

http://wumath.wustl.edu/files/math/SimpsonTI83.pdf

Answer 19

Wow. That's very useful indeed.