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Unformatted text preview: 1 2 x 2 d x = Z 6 x 26 x d x = Z 6 x 26 x + 2 d x = 2. If f ( x ) is negative on [ a, b ] , then R b a f ( x ) d x is negative. Why? Weren’t deﬁnite integrals deﬁned to be areas? (Review your deﬁnitions.) Sketch the following piecewisedeﬁned function, and evaluate the given deﬁnite integral in terms of area. Shade the regions whose areas you use to evaluate the deﬁnite integral. f ( x ) = √ 16x 2 x ≤ 42 x < x < 32 x ≥ 3 Z 44 f ( x ) d x = Suppose that f ( x ) is the velocity (in m/s) of an object at time x in minutes. What is the total distance traveled by the object on [4 , 2 ] ? Should Z 4 f ( x ) d x represent the total distance traveled by the object on [ 0 , 4 ] ? Think about what what a negative velocity means. . ....
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This note was uploaded on 05/27/2011 for the course MAC 2311 taught by Professor All during the Spring '08 term at University of Florida.
 Spring '08
 ALL
 Calculus, Riemann Sums, Angles

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