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Unformatted text preview: 1 2 x 2 d x = Z 6 x 2-6 x d x = Z 6 x 2-6 x + 2 d x = 2. If f ( x ) is negative on [ a, b ] , then R b a f ( x ) d x is negative. Why? Werent denite integrals dened to be areas? (Review your denitions.) Sketch the following piecewise-dened function, and evaluate the given denite integral in terms of area. Shade the regions whose areas you use to evaluate the denite integral. f ( x ) = 16-x 2 x 4-2 x < x < 3-2 x 3 Z 4-4 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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