calclec7

calclec7 - tom.h.wilson tom.wilson@mail.wvu.edu Dept....

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1 tom.h.wilson tom.wilson@mail.wvu.edu Tom Wilson, Department of Geology and Geography Dept. Geology and Geography West Virginia University Discussion of problems in Chapter 8 8.13 Tom Wilson, Department of Geology and Geography
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2 Problem 8.14 Tom Wilson, Department of Geology and Geography   cos   cos d We’re really asking “what is the integral?” 32 xx x  19 5 e x dx      19 5 ed the integral? Tom Wilson, Department of Geology and Geography 1 2 x e x 1 2 x e dx x
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3 From class notes last time: The velocity problem We’ve got an object traveling with velocity kt . Since v = dx/dt, we can rearrange and say dx vdt And to find out how far the object travels or where it’s going to be at a certain time, we sum up all the little steps: Tom Wilson, Department of Geology and Geography i.e. we take the integral . dx vdt The integral is just a sum of some quantity of interest when the steps are individually very very small. dx vdt  x vt  is really no different from In the case of the integral we’ve just let the steps become very very – infinitesimally – small: i.e. dx. We could play the mathematician and write this Tom Wilson, Department of Geology and Geography 11 () nn i ii x ki t t     2 1 n i kt i
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4 Going through the discrete sum - i.e. summing over steps that are small but not infinitesimally small – we get 22 (1 ) 2 n nn kt i kt 
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calclec7 - tom.h.wilson tom.wilson@mail.wvu.edu Dept....

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