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!

## Integral Problem? Can’t Figure It Out!?

April 21st, 2013 admin

put t=5. So simple

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 .

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!