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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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 Spring '08
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 Calculus, Riemann Sums, Angles, dx, Riemann sum, Total Distance, following piecewisedefined function

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