Integral Problem? Can’t Figure It Out!?

The sales of Universal Instruments in the first t years of its operation are approximated by the function
S(t) = t
(0.96t^(2) + 25)^(1/2)
where S(t) is measured in millions of dollars. What were Universal’s average yearly sales over its first 5 years of operation?
thank you so much in advance!

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3 Responses to “Integral Problem? Can’t Figure It Out!?”

  1. Rahul says:

    put t=5. So simple

  2. ted s says:

    ave S = [ 1 / 5 ] int over t in [ 0 , 5 ] of { t √ (0.96 t² + 25 ) dt }…..
    w² = 0.96 t² + 25 yields a polynomial to integrate .

  3. Renie says:

    Use the formula for average value of a function. 1/(b-a) * INT f(x) dx on [a,b]
    Integrate S(t) on the interval [0,5] and multiply by 1/5
    I am not sure of your function, but if S(t)= t* (.96t^2+ 25)^(1/2)
    Then (1/5)* INT [ (1/1.92)(1.92t)(.96t^2+ 25)^(1/2)] dt=
    (1/ 5)(1/1.92)(2/3) [ .96t^2+ 25)^(3/2)| [0,5]=
    = (2/28.8)[ ( .96* 25 + 25)^(3/2) – 25^(3/2)]
    = 545/136
    = 15.139 approximately
    (millions of dollars)
    I hope this helps!

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