Suppose that a a) Prove that if f is continuous at x0 [a, b] and f(x0) 0, then b) Show that if f

Suppose that a a) Prove that if f is continuous at x0 ˆˆ [a, b] and f(x0) ‰  0, then

b) Show that if f is continuous on [a, b], then ˆ«ba |f(x)dx = 0 if and only if f(x) = 0 for all x ˆˆ [a, b].
c) Does part b) hold if the absolute values are removed? If it does, prove it. If it does not, provide a counterexample.

dx > 0. f L)