Find the average value of the cost function C(x)=3x√x+10 on the interval [0,81].?

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Answer 1 · 2018-05-04T11:55:14

#Value_(avg)~~959.1#

#Value_(avg) = 1/(b-a)int_a^bf(x) dx#

In this case:

#Value_(avg)=1/(81-0)int_0^(81)3xsqrt(x+10)dx#

#=3/(81)int_0^(81)xsqrt(x+10) dx#

Let: #u=x+10, du=dx, x=u-10#:

#=1/(27)int_0^(81)(u-10)*u^(1/2) du#

#=1/(27)*2/(15) u^(3/2)(3u-50)[0,81]#

#=1/(27)*2/(15)(x+10)^(3/2)(3x-20)[0, 81]#

#=2/(405)[(223)(91)^(3/2)- (-20)(10)^(3/2)]#

#=2/(405)[20293sqrt(91)+200sqrt(10)]#

#~~959.1#