Find the average value h_{ave} of the function h on the given interval. NS

khi1la2f1qv 2021-11-16 Answered
Find the average value have of the function h on the given interval.
h(x)=8cos4(x)sin(x),[0,π]
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Expert Answer

Mary Darby
Answered 2021-11-17 Author has 11 answers
The given function h and the interval is,
h(x)=8cos4(x)sin(x),[0,π]
The average value of the function in the given interval is computed as follows.
have=1π00π8cos4(x)sin(x)dx
=8π0πcos4(x)sin(x)dx
=8π11u4du
Further evaluate the integral by using the property of the integrals as shown below.
have=8π11u4du
=8π(25)
=165π
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Drood1980
Answered 2021-11-18 Author has 16 answers
Consider the function
h(x)=8cos4xsinx
The average value of the function in the interval [0,π] is given by
have=1π00πh(x)dx
Hence,
have=1π00π8cos4xsinxdx
have=1π118t4dt
have=85π[t5]11
have=165π
Hence, the average value of the functions is have=165π
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