Unformatted text preview: the denominator has a very familiar interpretation. Consider one term of the sum in the denominator: (1 + x i )Δ x . This is the density near x i times a short length, Δ x , which in other words is approximately the mass of the beam between x i and x i +1 . When we add these up we get approximately the mass of the beam. Now each of the sums in the fraction has the right form to turn into an integral, which in turn gives us the exact value of ¯ x : ¯ x = Z 10 x (1 + x ) dx Z 10 (1 + x ) dx ....
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 Spring '07
 JonathanRogawski
 Math, Calculus, Center Of Mass, Elementary arithmetic, Sexagesimal

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