Unformatted text preview: B. Find the general antiderivative of f ( x ) =  x  3 . C. Does the “greatestinteger function” f ( x ) = [ x ] (where [ x ] is deﬁned as the greatest integer n satisfying n ≤ x ) have an antiderivative? Explain. D. (a) Show that if f is odd, then every antiderivative of f is even. (Hint: We must show that if f ( x )+ f (x ) = 0 for all x and F ( x ) = f ( x ) for all x , then F (x ) = F ( x ) for all x .) (b) Show that if f is even, and f has an antiderivative, then f has exactly one antiderivative that is odd. Please don’t forget to write down on your assignment who you worked on the assignment with (if nobody, then write “I worked alone”), and write down on your timesheet how many minutes you spent on each problem (this doesn’t need to be exact)....
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This note was uploaded on 02/13/2012 for the course MATH 141 taught by Professor Staff during the Fall '11 term at UMass Lowell.
 Fall '11
 Staff
 Math, Calculus

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