My question is:
Let V = \mathbb{R}_1 [x] be the vector space of polynomials in x of degree at most 1. For f(x) \, , \, g(x) \in \mathbb{R}_1 [x], define:
<f(x) \, , \, g(x)> \, = \int_0^1 x^2 f(x) g(x) dx
Show that this defines an inner product on \mathbb{R}_1[x]. (You may assume...