Section 5.2 Q 31

Stuck on what might be another typo!

31a)

Firstly to calculate the analytical result if you integrate x³ you get x⁴/4.
Then use x = 0.5 to get 0.015625. The book says the result SHOULD be 0.015225

Already alarm bells are ringing.

f''(x) = 6x

To perform the trapezoidal rule, you need some value for h or n. This is not supplied in the question anywhere!

How does one complete this question?

I get the same result as the book for the exact result, but that seems pretty pointless in a course on numerical methods unless we're given some approximation to compare.

Take h to be some number you're fond of, do a Trapezoidal approx. on the same integral (pretending you don't know you can do it analytically), and you should get a bit of error.

Then one could set this exact known error equal to the error expression and solve?

Without inventing h, I can't see how to do a Trapezoidal. Maybe just do that.

In fact how about starting with h n = 2 3? That's the bare minimum to have a meaningful "global" error. I think I'll go do that and report back.

(Adjusted that). If you set n = 3 (by making h = 0.1) you get an estimate of:

0.1/2[0.2³ + 2(0.3³) + 2(0.4³) + 0.5³] = 0.0126716

And that can be subtracted from the exact figure to give you something to solve the error expression for.

My point is they chose some h and concluded an answer. Is this something that could happen in the exam? How did they arrive at h?

No they didn't choose h to reach the answer. It's worse than that.

The answer is the correct solution to the exact analytical solution (plug in and you'll see).

My point is it's probably best to try and make the best of a bad thing, and get something out of it nevertheless?

EDIT: And as for the exam, I think you can reasonably expect it to be fairly "evil". Certainly if Oct 2010 is anything to go by.

Just as a matter of interest, how would you go about tackling Q1 of that paper? (It completely floors me, still, even with a relatively large amount of time available).

Hey, I don't have Oct 2010. Could you e-mail it through to me?

Done.

In Durban quite a lot of people got bored with this paper about half way through, last year.

Are you in Durban?

[Edit] E-mail never came through. Will PM you my e-mail address again....

We've had a dead phone for most of the morning. That might be the problem. See PM. I'll check my inbox on the way out of here. (I used your old email and pushed reply, so there shouldn't be an email problem). You have the Oct 2010 paper, though?

Negative. No October 2010 paper still. Please check its left your outbox....