How do you find the average value of sin ⁡ x as x varies between [ 0 , π ]?

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How do you find the average value of   sin  ⁡  x as x varies between   [  0  ,  π  ]?

Jaida Sanders · Accepted Answer

Explanation:The average value of a function f on the interval [a,b] is found through the integral expression      1          b      −      a            ∫          1              b        f  (  x  )  d  xHere, this gives us an average value of      1          π      −      0            ∫          0              π        sin  ⁡  (  x  )  d  xThe antiderivative of   sin  ⁡  (  x  ) is   −  cos  ⁡  (  x  )  :  =      1    π    [  −  cos  ⁡  (  x  )      ]          0              π        =      1    π    (  −  cos  ⁡  (  π  )  −  (  −  cos  ⁡  (  0  )  )  )  =      1    π    (  −  (  −  1  )  −  (  −  1  )  )  =      2    π

How do you find the average value of sin ⁡ x as x varies between...

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