Question
Asked Feb 20, 2020
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Consider the given function and the given interval.
f(x) = 18 sin(x) – 9 sin(2x), [0, x]
(a) Find the average value fave of f on the given interval.
fave
%3D
(b) Find c such that fave = f(c). (Round your answers to three decimal places.)
(smaller value)
(larger value)
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Consider the given function and the given interval. f(x) = 18 sin(x) – 9 sin(2x), [0, x] (a) Find the average value fave of f on the given interval. fave %3D (b) Find c such that fave = f(c). (Round your answers to three decimal places.) (smaller value) (larger value)

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Expert Answer

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Step 1

                Average value fave of f(x) on the given interval [a, b] is given by -

                                        Calculus homework question answer, step 1, image 1

                                           Difference rule of integration is given by –

                                            Calculus homework question answer, step 1, image 2

                                           

                                              

        

Step 2

     

Given – 

     a)                       Calculus homework question answer, step 2, image 1

                              Calculus homework question answer, step 2, image 2

                              Substituting given values of f(x), a and b in the formula.

                                Calculus homework question answer, step 2, image 3

                                  Using a difference rule of integration can be rewritten as

                                  Calculus homework question answer, step 2, image 4

                                            Calculus homework question answer, step 2, image 5

                                            Calculus homework question answer, step 2, image 6

                                            Calculus homework question answer, step 2, image 7

                                            

                                              

Step 3

b)               We have to find c such that favg =f(c)

                   Substituting x = c in f(x) we will get

                     Calculus homework question answer, step 3, image 1

                        So according to the question

                          Calculus homework question answer, step 3, image 2  

                 Using graphing calculator we can find two values of c

                        Calculus homework question answer, step 3, image 3

             ...

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