first let me start by apologizing if this question has been asked before, but i've never studied math in english and am lacking the language to formulate a proper search string, and now onto the question:
let $V$ be a vector space of the real polynomials where the following is true: $f(-1)=f(1)=0$
the inner product is defined as: $\langle f, g \rangle = \displaystyle\int_{-1}^{1} f(x)g(x)dx$
i need to find a orthonormal base for $V$. i can't seem to figure out how to use f(-1)=f(1)=0 some one told me that it is supposed to help me pick a base, but i don't see how, any sort of hint/solution would be greatly appreciated
note: i found this question which seems to be almost identical but without $f(-1)=f(1)=0$