Use the fundamental theorem of calculus to evaluate f'(x), where f(x) = * log(1 + t)dt....

 

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Use the fundamental theorem of calculus to evaluate f'(x), where f(x) = ²* log(1 + t)dt. (b) Suppose f and g are continuous functions on [a, b] such that få ƒ = fg. Prove there exists x in (a, b) such that f(x) = g(x). (c) Define f: [a, b] → R by f(x) = 9 if x = [a, b] nQ and x = otherwise. Show that f is integrable and compute f f(x) dx. with p, q coprime, Use the fundamental theorem of calculus to evaluate f'(x), where f(x) = ²* log(1 + t)dt. (b) Suppose f and g are continuous functions on [a, b] such that få ƒ = fg. Prove there exists x in (a, b) such that f(x) = g(x). (c) Define f: [a, b] → R by f(x) = 9 if x = [a, b] nQ and x = otherwise. Show that f is integrable and compute f f(x) dx. with p, q coprime,

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a Using the fundamental theorem of calculus we may determine the value of fx where fx 0x x2 log1t dt If Fx is the integral of ft then its derivative with respect to x is equal to fx as stated by the t... View the full answer