Question

Find the average value of the function on the given interval. f(x)=6x lnx; [1,e^2]

Answer 1

average value is area under the curve divided by the interval length

what do you get?
Use integration by parts for x lnx

Answer 2

(1/e^2-1)(6x^2 lnx/2-x^2/4)
am I on the right track?

Answer 3

Integrate the function over that interval and divide the integral by e^2 - 1.

Try integration by parts for the integral.
Let lnx = u and dv = 6 x dx
du = dx/x and v = 3 x^2

Integral of f(x) dx =Integral u dv
= uv - Integral v du
= 3 x^2 lnx - Integral of 3x dx
= 3x^2 lnx - (3/2)x^2

Answer 4

so my answer would be 3/2 (3e^4+1)/ (e^2-1)?

Answer 5

That is correct.