For positive integers n ≥ 1, consider the functions 2 A (a) Show that (b) Show that Sn(x) = ㅠ [ Sn = sin(nx) [" (5(2))² de 1 for all n. da dx = Sn(x) Sm(x) dx = 0 for all n m.

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A: We can answer the question as below using the properties of definite integral.

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