Explanation 1) Concept: Use the formula for the average value of g on the interval [ a , b ] . 2) Formula: g a v e = 1 b - a ∫ a b g ( x ) d x 3) Given: g x = 3 cos ⁡ x , [ - π / 2 , π / 2 ] 4) Calculation: Here, g x = 3 cos ⁡ x , a = - π / 2 and b = π / 2 , g a v e = 1 π 2 - ( - π 2 ) ∫ - π / 2 π / 2 ( 3 cos ⁡ x ) d x = 1 π ∫ - π / 2 π / 2 ( 3 cos ⁡ x ) d x Since cos ⁡ x is an even function, its multiple is also an even function

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Author: James Stewart

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Chapter 5.5, Problem 3E

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The average value of the given function on the given interval.

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The average value of the given function on the given interval.

Solution Summary: The author explains the formula for the average value of g on the interval [a,b].

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To find: The average value of the given function on the given interval.

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Chapter 5 Solutions

To find:

The average value of the given function on the given interval.