Suppose that f : [a, b] R is continuous and that for all integers n > 0. a) Evaluate ba P(x) f(x) dx for

Suppose that f : [a, b] †’ R is continuous and that

for all integers n > 0.
a) Evaluate ˆ«ba P(x) f(x) dx for any polynomial P on R.
b) Prove that ˆ«ba|f(x)|2 dx = 0.
c) Show that f(x) = 0 for all x ˆˆ [a, b].

x"f(x) dx=0