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28B MVT Integrals
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Mean Value Theorem for Integrals
28B MVT Integrals
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Definition Average Value of a Function
If f is integrable on [a,b], then the average value of f on [a,b] is
EX 1 Find the average value of this function on [0,3]
28B MVT Integrals
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Mean Value Theorem for Integrals
If f is continuous on [a,b] there exists a value c on the interval (a,b) such that
.
28B MVT Integrals
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EX 2 Find the values of c that satisfy the MVT for integrals on [0,1].
EX 3 Find values of c that satisfy the MVT for
integrals on [3π/4 , π].
f(x)=cos(2x-π)
28B MVT Integrals
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Symmetry Theorem
If f is an even function, then .
If f is an odd function, then .
Theorem
If f is a periodic function with period p, then .
28B MVT Integrals
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EX 4
EX 5
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