# Any help understanding this Lemma is Appreciated!

1. Mar 12, 2012

### Mining_Engr

The lemma and proof are attached, how does the hypothesis imply that ∫h(u)*p(u)du = 0. This is where I am hung up. I don't see how the hypothesis implies this, please help!

Mining_Engr

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2. Mar 12, 2012

### Office_Shredder

Staff Emeritus
p(u) is a polynomial, say
$$p(u) = \sum_{i=0}^n \alpha_i u^i$$

then
$$\int h(u) p(u) du = \int h(u) \sum_{i=0}^n \alpha_i u^i du = \sum_{i=0}^n \alpha_i \int h(u) u^i du$$
and all those integrals at the end are zero so the whole sum is zero