Notes 8AV (Average Value)

Notes 8AV (Average Value) - MIT OpenCourseWare...

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MIT OpenCourseWare 18.01 Single Variable Calculus Fall 2006 For information about citing these materials or our Terms of Use, visit: .
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AV. AVERAGE VALUE What was the average temperature on July 4 in Boston? T T The temperature is a continuous function f(z), whose graph over the 80 24-hour period inight look as shown. How should we define the average value of such a function over the time interval [0, 24] -- measuring time s in hours, with z = 0 at 12:00AM ? 6 12 18 24 x We could observe the temperature in the middle of every hour, that is, at the times zX = .5,zs = 1.5,. .. ,z4 = 23.5, then average these 24 observations, getting 1 24 =1 To get a more accurate answer, we could average measurements made more frequently, say every ten minutes. For a general interval [a, b] and function f(z), the analogous procedure would be to divide up the interval into n equal parts, each of length b-a (1) A. = - n and average the values of the function f(x) at a succession of points
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This note was uploaded on 10/10/2011 for the course MATH 31 taught by Professor Blake during the Spring '11 term at MIT.

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Notes 8AV (Average Value) - MIT OpenCourseWare...

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