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13 Nov 2019

# Consider the following proof of the mean value theorem for definite integrals: Let F(x)=SSodt, asxsb. By the Fundamental Theorem of Calculus, F(x) is continuous on [a,b], differentiable in (a,b) with F'(x) = f(x), and F(b) - F(a) = f(x)dx Hence by Lagrange mean value theorem, there exists ce(a,b) such that fe) = F'(C)= F(b)-F(a) - 1Å¿' f(x)dx 25 b-ab-ala Is there any problem with this proof? If so, briefly explain why.

Consider the following proof of the mean value theorem for definite integrals: Let F(x)=SSodt, asxsb. By the Fundamental Theorem of Calculus, F(x) is continuous on [a,b], differentiable in (a,b) with F'(x) = f(x), and F(b) - F(a) = f(x)dx Hence by Lagrange mean value theorem, there exists ce(a,b) such that fe) = F'(C)= F(b)-F(a) - 1Å¿' f(x)dx 25 b-ab-ala Is there any problem with this proof? If so, briefly explain why.

Jarrod RobelLv2

26 Mar 2019