# Cos 5 x 2 2x 4x cos 5 x2 13 false you should realize

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cos5(-x2)·(-2x)= 4xcos5(x2)13False. You should realize that definite integrals evaluated at constant endpointsaandbareconstant, and in order to apply the Fundamental Theorem at least one of the endpoints as avariable.14The answer is(b).This problem should help you realize that an integral of this form is aspecific function (not a general anti-derivative), and the integrand is its derivative. You caninduce information about the concavity ofgjust like you normally would with any otherfunction, only that this time you have to look atf.15Answers:g(0) = 0,g0(0) =f(0) = 4, andg0(2) =f(2) = 0.16All do.Notice we’re using the standard definition of the average velocity (that’s (b)), theMean Value Theorem (that’s (c)) and also the representation of total distance traveled fromintegration (and that’s (a)).