Suppose that h_n is a sequence of non-negative integrable functions on [a,b], su

Question

Suppose that h_n is a sequence of non-negative integrable functions on [a,b], such that the limit of the integral (from a to b) of h_n(x)*dx = 0 (as n goes to infinity).
(a)Show that if f is integrable on [a,b], then the limit of the integral (from a to b) of f(x)*h_n(x)*dx = 0 (as n goes to infinity).
(b)Use this result to show that if f is integrable on [0,1], then the integral (from 0 to 1) of x^(n)*f(x)*dx = 0

I broke up the last part from the first, but i'm hoping someone

can help explain the first part?

Explanation / Answer

math.gmu.edu/~dwalnut/teach/Math776/Spring11/776s11lec10...

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