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Unformatted text preview: closed interval [ a, b ], then the area of the region bounded by the graph of f , the xaxis, and the vertical lines x = a and x = b is given by f (x)dx a b Defn. of 2 Special Definite Integrals 1. If f is defined at x = a, then 2. If f is integrable on [a, b], then f (x)dx a a = 0 f (x)dx a =  f (x)dx a b Thm. 4.6 Additive Interval Property If f is integrable on the three closed intervals determined by a, b, and c, then f (x)dx a b = f (x)dx a c + f (x)dx c b Properties of Definite Integrals Preservation of Inequality 1. If f is integrable and nonnegative on the closed interval [ a, b ], then 2. If f and g are integrable on the closed interval [ a, b ] and f(x) < g(x) for every x in [ a, b ], then f (x)dx a b 0 < f (x)dx a b < g (x)dx a b Joke Time What do you call 2 spiders who just got married? Newlywebs What did the Atlantic Ocean say to the Pacific Ocean? Nothing, they just waved....
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 Fall '08
 JARVIS
 Calculus, dx, subinterval

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