That is okay, I hope you are feeling better. If not then get some rest and we can continue later or tomorrow.

Your answer is correct! We use this formula to get more.

Agnishom wrote:

n is the number of intervals or something like that I suppose?

How do you get this formula?

bobbym wrote:

Hi;

Yes, n is the number of intervals. The formula is derived in a lot of books. I am not that big on memorizing proofs or derivations so I do not recall it offhand. What is important for numerical work is the error estimate and the fact that it works!

This is known as the *Trapezium Rule*. Proving it can be done as follows.

It can be shown that

where U(f,P) and L(f,P) are the lower Darboux sums of f with respect to the partition P, defined by

and M_i and m_i are given by their usual definitions

Then, it is easy to see that

.A similar technique is used to show that a monotonic function on [a,b] is Riemann integrable on [a,b].

]]>Unless he wants an numerical integration method.

]]>You can use this fact:

I would not recommend it, though.

]]>How do I evaluate this?

]]>But needs much practice to know the rules and use it efficiently.

]]>I have learned a bit about it, I was amazed by how simple and complex it looks at the same time. Also, the tacit programming part of J caught my eye. I haven't done much in it though.

]]>I'm still learning. Are you too trying out J?

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