For the following exercises, consider the functions f(x) = sin(x) and g(x) = x² Theorem 1. If the derivative g' exists and is continuous in J and if f is integrable with respect to g then the product fg is integrable and: Theorem 2. If f is integrable with respect to g, then g is integrable with respect to g and: b [rag=fra dg 1.sin(x) dg Calculate the following Reimann-Stieltjes integrals. 2. f x² df b b fras 1 ƒ dg = f(b)g(b) – f(a)g(a) – [g df a a (Here you could use theorem 1) (Here you could use theorem 1 or theorem 2) Please be as clear as posible, legible, and showing and explaining all the steps. Thank you very much.

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