Given a function f deﬁne a new function Sf(x) by summing up all values of f(hj)(adsbygoogle = window.adsbygoogle || []).push({});

where 0 ≤ jh < x. That is, if k is such that kh is the largest below x, then

Sf(x) = h[ f(0) + f(h) + f(2h) + .... + f(kh) ]

We call Sf also the ”integral” or ”antiderivative” of f.

The teacher who wrote the lecture notes I'm reading through gives an example of integration. He evaluates Sf(x) for f(x)=1. I don't understand the first sentence:

We have Sf(x) = 0 for x ≤ h.

Why? Sorry for being such a n00b, but I don't understand. Please help me.

Thanks,

Mathguy

By the way, he verifies that the js in the definition are integers.

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# Another really basic question... this time regarding integration.

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