Simpson's Rule / Trapezoidal Rule Issues. (1 Viewer)

[Brad.1990]

SOMEONE. Can you explain to me hwo to apply these rules to equations.

The question that is annoying me is:
Find Intergral endpoints 7 and 1, x - 1 / x + 1 dx, using Simpson's Rule with 5 function values.

The answer I got was 1.915.

I am almost positive this is incorrect.

HELP SOMEONE! Plz

 

[lyounamu]

SOMEONE. Can you explain to me hwo to apply these rules to equations.

The question that is annoying me is:
Find Intergral endpoints 7 and 1, x - 1 / x + 1 dx, using Simpson's Rule with 5 function values.

The answer I got was 1.915.

I am almost positive this is incorrect.

HELP SOMEONE! Plz

6/4 = 1.5

x= 1 so y=0
x=2.5 y=3/7
x=4 y=3/5
x=5.5 y=9/13
x=7 y=6/8

A = (approximately equal to) 1.5/3 (0+6/8+4(3/7 + 9/13) + 2(3/5))
= 3.21675824...

 

[danz90]

A common problem I used to have with Simpson's rule.. is that I used to assign the following to each function value:

x0, x1, x2, x3 and so on... so that I could easily determine which is even or odd etc. But then, if you use that kind of 'labelling' of function values, you have to change the formula a little (i.e. 4(odd) + 2(even) instead of 4(even) + 2(odd) ). That's why, make sure you label as x1, x2, x3... and so on.. to use the following formula:

A = h/3 (f(1st fn value) + f(last fn value) + 4(even) + 2(odd) )

lol hope that makes sense.

 

[lyounamu]

A common problem I used to have with Simpson's rule.. is that I used to assign the following to each function value:

x0, x1, x2, x3 and so on... so that I could easily determine which is even or odd etc. But then, if you use that kind of 'labelling' of function values, you have to change the formula a little (i.e. 4(odd) + 2(even) instead of 4(even) + 2(odd) ). That's why, make sure you label as x1, x2, x3... and so on.. to use the following formula:

A = h/3 (f(1st fn value) + f(last fn value) + 4(even) + 2(odd) )

lol hope that makes sense.

Are you referring to my working out?

 

[danz90]

Are you referring to my working out?

Nah, you're working is perfect... just in general.. I experienced some problems with Simspon's Rule because of what I stated in my above post (about labelling of function values).

 

[PC]

I always do Simmo's Rule or Trap Rule by using tables.

x f(x) W P
1 0.0000 1 0.0000
2.5 0.4285 4 1.7142
4 0.6000 2 1.2000
5.5 0.6923 4 2.7692
7 0.7500 1 0.7500

Sum of P column = 6.4332

Then Integral = 1/3 x h x sum of P
= 1/3 x 1.5 x 6.4332
= 3.2167

For Trap Rule it's exactly the same, except the Weightings (W) are 1, 2, 2, ..., 1 and the last bit is 1/2 x h x sum of P.

Easy and very neat way of doing it. Very few calculator errors.

 

[Brad.1990]

Thanks.
I kind of get it.
=]