Numerical integration Trapezium rule and method of undetermined coefficients

http://i.imgur.com/SHnlHCM.png

That is the question I'm trying to finish, I've done parts (a) and (b) and the first part of (c). The bit that I'm struggling with is the highlighted part.

So I've assumed the error term is of the form that was given. So I need to get a function f and take the fourth derivative. I'm thinking this will have to end up being a constant so that epsilon (sorry dont know the actual name of the greek letter) can disappear.

Would I just need to let f(x) = x4 ? That just doesn't seem right to me..

Also have one more question, how would you use the trapezium rule to approximate an integral? E.g. integrate sin(x) from 0 to pi

When I apply the trapezium rule I get 0..

Reply 1

DFranklin

18

Original post by 0range

http://i.imgur.com/SHnlHCM.png

That is the question I'm trying to finish, I've done parts (a) and (b) and the first part of (c). The bit that I'm struggling with is the highlighted part.

So I've assumed the error term is of the form that was given. So I need to get a function f and take the fourth derivative. I'm thinking this will have to end up being a constant so that epsilon (sorry dont know the actual name of the greek letter) can disappear.

Would I just need to let f(x) = x4 ?

Yes, should be fine.

Also have one more question, how would you use the trapezium rule to approximate an integral? E.g. integrate sin(x) from 0 to pi

When I apply the trapezium rule I get 0..

Use a lot more ordinates. Subdivide into 16 intervals and you should get a much closer result.