Find c such that fave =f(c), f(x)=(x-3)^{2}, [2,5]

Joan Thompson 2021-12-20 Answered
Find c such that fave =f(c),f(x)=(x3)2,[2,5]
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Expert Answer

alexandrebaud43
Answered 2021-12-21 Author has 36 answers

Average value of the function f(x) over the interval [a,b] is given by
favg=1baabf(x)dx
Average value of f(x)=(x3)2 ovthe interval [2,5] is given by
favg=15225(x3)2dx
Substitutex3=u and dx=du
Limits of Integration will change from 252353=12
=1312u2du
=13[u33]12
=13[83+13]=1

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Orlando Paz
Answered 2021-12-22 Author has 42 answers

Average value of the function f(x) over the interval [a,b] is given by
favg=1baabf(x)dx
Average value of f(x)=(x3)2 over the interval (2,5] is given by
favg=15225(x3)2dx
=13[(x3)33]25
=13[83+13]=13×93=1

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