# Exercise 1: For the following statements, say true or false. If true, provide a brief reason. If false, provide acounterexample.(a) If f and g are integrable on [a, b], and g(x) # 0 on [a, b], then f/g is integrable on [a, b].(b) Suppose for all a, b e R, ƒ and g are integrable on [a, b]. If Sº f = L° g for all a, b, then f = g.(c) If f is integrable on [a, b], then F(x) = S* f(t) dt is continuous on [a, b].(d) If ƒ is strictly increasing and integrable on [a, b], and a < c < b, then , f(t) dt < [, f(t) dt.(e) Suppose f and g are integrable on [a, b] and for all c e (a,b), S. f(t) dt < S g(t) dt. Thenf(x) < g(x).

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Asked Jan 16, 2020
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Hi! Your question is having multiple sub-parts. Since nothing is specified, we are answering only the first question. So, if you need the solution for other sub-parts then kindly post this question again with the specification of required sub-parts.

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We need to identify whether the statements are true or false with proper justifications.

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MathCalculus