Posted by Jane on Saturday, November 26, 2011 at 5:51pm.
Find the average value of the function on the given interval. f(x)=6x lnx; [1,e^2]

Calculus  Steve, Saturday, November 26, 2011 at 5:57pm
average value is area under the curve divided by the interval length
what do you get?
Use integration by parts for x lnx

Calculus  Jane, Saturday, November 26, 2011 at 6:07pm
(1/e^21)(6x^2 lnx/2x^2/4)
am I on the right track?

Calculus  drwls, Saturday, November 26, 2011 at 6:14pm
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

Calculus  Jane, Saturday, November 26, 2011 at 6:26pm
so my answer would be 3/2 (3e^4+1)/ (e^21)?

Calculus  Steve, Sunday, November 27, 2011 at 12:57pm
That is correct.
Answer This Question
Related Questions
 Calculus  I'm supposed to find the average value of the function over the given...
 calculus  Consider the given function and the given interval. f(x) = 4 sin x &#...
 Math  Find the average value of the function over the given interval and all ...
 Calculus  Given k(p) = p+4, find the average value of this function on the ...
 Calculus  Find the average value of the function on the given interval: f(x) = ...
 calculus  Find the average value of the function on the given interval f(x) = ...
 Calculus  Find the average value of the function f(x) 8x^29x+8 on the interval...
 Calculus  Find the average value of the function on the given interval: f(x)=...
 Calculus  Find the average value of the function over [1,3] and all values of x...
 calculus  Consider the function f(x)=–3x3–1x2+1x+1Find the average slope of ...
More Related Questions