13 - AverageValue

13 - AverageValue - r on the interval[e e d Ex Find the...

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Average Value Suppose we want to find the average temperature over a 24 hour period. We will take n measurements so Average temperature = T ( t 1 ) T ( t 2 ) ... T ( t n ) n Since the more measurements we take the better the approximation, we will rewrite this expression as a Riemann sum over 0 t 24. Recall that t 24 n so n 24 t . Average temperature = T ( t 1 ) T ( t 2 ) ... T ( t n ) 24 t = 1 24 T ( t 1 ) T ( t 2 ) ... T ( t n ) ) t = 1 24 T ( t i ) i 1 n t lim n 1 24 T ( t i ) t i 1 n 1 24 T ( t ) dt 0 24 In general the average value of f from a to b is 1 b - a f ( x ) dx a b
Ex. Find the average value of f(x) = (x – e)

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Unformatted text preview: r on the interval [e, e+d]. Ex. Find the average value of f ( x ) cos x 3 8 x 2 3 on [0, 8]. Do: Find the average value of f ( x ) 2 x-3 3 on [1, 4]. Mean Value Theorem: If f is continuous on [a, b], there exists a number c in [a, b], such that f ( c ) 1 b-a f ( x )± dx a b . Ex. f(x) = x 2-1 ≤ x ≤ 1 Ex. f(x) = (x – e) r [e, e + d] Ex. f ( x ) 1 x ±±±±±±[1, 3]...
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