L30 - of equal width and x * i = left endpoint. 5 Let x * i...

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L30 – Area and Distance R n – sum of the areas of n rectangles each of equal width and height R n = 1
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If n = 4, R n = If n = 8, R n = lim n →∞ R n = as n → ∞ R n so we define area to be 2
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In general, divide [ a,b ] into n subintervals using partition a = = b Subintervals: Widths: as the number of subintervals gets larger and widths get smaller the approximation gets better so A = (if f is continuous this limit exists so that the region has area) 3
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In general, A = We use sigma notation to express this more concisely as A = 4
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Estimate the area under f ( x ) = x 3 +1 from x = 0 to x = 3 using six subintervals
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Unformatted text preview: of equal width and x * i = left endpoint. 5 Let x * i = right endpoint Use the midpoint with 3 subintervals. 6 Find an expression for the exact area under f ( x ) = x 3 + 1 from x = 0 to x = 3 using n subintervals of equal width and x * i = right endpoint. 7 Distance Find the distance travelled by an object during a certain time period if the velocity is known at all times. 8 What area is represented by lim n →∞ n X i =1 (1 + 3 i n ) 2 ( 3 n ) 9...
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This note was uploaded on 01/13/2010 for the course MAC 2311 taught by Professor All during the Fall '08 term at University of Florida.

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L30 - of equal width and x * i = left endpoint. 5 Let x * i...

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