Let g [a, b] R be dif- ferentiable and assume g' is continuous. Let f [c,...

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Let g [a, b] R be dif- ferentiable and assume g' is continuous. Let f [c, d] → R be continuous, and assume that the range of g is contained in [c, d] so that the composition fog is properly defined. (a) Why are we sure f is the derivative of some function? How about (fog)g'? (b) Prove the change-of-variable formula [ f(g(x))g'(x)dx= a (9(b) •Soc f(t)dt. g(a) = Let g [a, b] R be dif- ferentiable and assume g' is continuous. Let f [c, d] → R be continuous, and assume that the range of g is contained in [c, d] so that the composition fog is properly defined. (a) Why are we sure f is the derivative of some function? How about (fog)g'? (b) Prove the change-of-variable formula [ f(g(x))g'(x)dx= a (9(b) •Soc f(t)dt. g(a) =