lecture33

lecture33 - Â 6.5 Applications of the Definite Integral...

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Unformatted text preview: Â§ 6.5 Applications of the Definite Integral Math 121 Lecture 33 ! Average Value of a Function Over an Interval ! Consumersâ€™ Surplus (*) ! Future Value of an Income Stream ! Volume of a Solid of Revolution Determine the average value of f ( x ) = 1 â€“ x over the interval -1 ! x ! 1. Using (2) with a = -1 and b = 1, the average value of f ( x ) = 1 â€“ x over the interval -1 ! x ! 1 is equal to An antiderivative of 1 â€“ x is . Therefore, So, the average value of f ( x ) = 1 â€“ x over the interval -1 ! x ! 1 is 1. ( Average Temperature ) During a certain 12-hour period the temperature at time t (measured in hours from the start of the period) was degrees. What was the average temperature during that period? The average temperature during the 12-hour period from t = 0 to t = 12 is ( Average Temperature ) During a certain 12-hour period the temperature at time t (measured in hours from the start of the period) was degrees....
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This document was uploaded on 09/30/2010.

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lecture33 - Â 6.5 Applications of the Definite Integral...

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