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.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Another really basic question this time regarding integration.

**Physics Forums | Science Articles, Homework Help, Discussion**