Find the average value fave of the function f on the given interval. f (...

Ramiro Wise

Ramiro Wise

Answered

2022-11-28

Find the average value fave of the function f on the given interval.
f ( t ) = e sin ( t ) , cos ( t ) , [ 0 , π 2 ]

Answer & Explanation

rezvanifanFdT

rezvanifanFdT

Expert

2022-11-29Added 9 answers

The average value of a function over an interval [ a , b ] is given by
1 b a a b f ( x ) d x
We have
1 π 2 0 0 π / 2 e sin t cos t d t = 2 π 0 π / 2 e sin t d ( sin t ) = 2 π sin 0 sin ( π / 2 ) e u d u = 2 π e u | sin 0 sin ( π / 2 ) = 2 ( e 1 e 0 ) π = 2 ( e 1 ) π

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