Trapezoidial and mid ordinate?

[LukeGernon]

anyone willing to show me how this done?

 

[Deleted member 4993]

anyone willing to show me how this done?

Yes ....but you have to show your work so that we know where do we start and where/why are you stuck!

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

https://www.freemathhelp.com/forum/threads/read-before-posting.109846/#post-486520

Please share your work/thoughts about this problem.

 

[Dr.Peterson]

anyone willing to show me how this done?

You can probably see examples of how it is done in your textbook. If not, try this one. (I'm assuming your mid-ordinate rule is the same as the midpoint rule.)

 

[LukeGernon]

here are my results if someone could tell me if I'm correct ild appreciate I have no tutors around to proof read

 

[LukeGernon]

Yes ....but you have to show your work so that we know where do we start and where/why are you stuck!

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

https://www.freemathhelp.com/forum/threads/read-before-posting.109846/#post-486520

Please share your work/thoughts about this problem.
View attachment 21761

very stuck on Simpsons rule its result comes nowhere near my mid ordinate and trap answers. I have re worked the trap rule now to get an A=0.6718 Which seems to be pretty accurate and mid ordinate off A=0.6389 but Simpsons = 0.8279 which can't be correct surely?

 

[Dr.Peterson]

here are my results if someone could tell me if I'm correct i'd appreciate I have no tutors around to proof read

I've taken a look, making a spreadsheet to avoid errors.

In the original trapezoidal rule work, you accidentally used x (0.1745) instead of y (0.4167) for the first nonzero term.

very stuck on Simpsons rule its result comes nowhere near my mid ordinate and trap answers. I have re worked the trap rule now to get an A=0.6718 Which seems to be pretty accurate and mid ordinate off A=0.6389 but Simpsons = 0.8279 which can't be correct surely?

For the trapezoidal rule, I get 0.672113. The difference is due to rounding in your work.

For Simpson, you seem to have added on an extra "last" point. The last should be x_6 = 1.047, and you should have 3 even and 2 odd points. The way I did it, I multiplied the 7 y values respectively by 1, 4, 2, 4, 2, 4, 1 and added them up.

 

[jonah2.0]

Beer induced programming follows.
As I said at the other site, you could also automate these approximation(s) with a scientific calculator's sigma function for double checking your work. Thus, for Simpson's Rule:
[MATH]\frac{1}{3}*\frac{b-a}{n}\bigg(\sum_{i=0}^{n}\sqrt{\sin\bigg(a+\frac{b-a}{n}*i\bigg)}+\sum_{i=1}^{n-1}\sqrt{\sin\bigg(a+\frac{b-a}{n}*i\bigg)} +2*\sum_{i=1}^{n/2}\sqrt{\sin\bigg[a+\frac{b-a}{n/2}\bigg(i-\frac{1}{2}\bigg)\bigg]}\bigg)[/MATH]
Try downloading scientific calculator apps like "Free scientific calculator plus advanced 991calc".