Chap6_Sec5

# Chap6_Sec5 - 6 APPLICATIONS OF INTEGRATION APPLICATIONS...

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APPLICATIONS OF INTEGRATION APPLICATIONS OF INTEGRATION 6

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6.5 Average Value of a Function In this section, we will learn about: Applying integration to find out the average value of a function. APPLICATIONS OF INTEGRATION
It is easy to calculate the average value of finitely many numbers y 1 , y 2 , . . . , y n : 1 2 n ave y y y y n + +××× + = AVERAGE VALUE OF A FUNCTION

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However, how do we compute the average temperature during a day if infinitely many temperature readings are possible? AVERAGE VALUE OF A FUNCTION
This figure shows the graph of a temperature function T ( t ), where: t is measured in hours T in ° C T ave , a guess at the average temperature AVERAGE VALUE OF A FUNCTION

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In general, let’s try to compute the average value of a function y = f ( x ), a x b . AVERAGE VALUE OF A FUNCTION
We start by dividing the interval [ a, b ] into n equal subintervals, each with length . ( ) / x b a n ∆ = - AVERAGE VALUE OF A FUNCTION

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x 1 * , . . . , x n * in successive subintervals and calculate the average of the numbers f ( x i * ), . . . , f ( x n * ): For example, if f represents a temperature function and n = 24, then we take temperature readings every hour and average them. AVERAGE VALUE OF A FUNCTION
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Chap6_Sec5 - 6 APPLICATIONS OF INTEGRATION APPLICATIONS...

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