3a. " Let fn : [0, 1] - R be defined by fn (x) = n2x (1 - x)". Is is true that lim n-co Jo fn (x) dx = lim fn (x) dx n-00 Hint: Show that So fn(x) dx = n2 (n+1)(n+2) and fn - f = 0 pointwise. 3b. Let fn (2) = 1 Itx2+ 26, * 6 0, 1. Find lim fn (x) dx n-+0o Justify your answer. Hint: First show that fn - f uniformly where f(x) := 14 (try to prove that Ifn(x) - f(x) | 5 2), then use the Proposition 0.6 of the Lecture Note 17