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Find f(4) if f(x) is defined by:

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I got this far:
|dw:1353113577149:dw| I am not sure if I can apply the fundamental theorem of Calculus here...

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I believe that you can apply the Fundamental Theorem of Calculus here if you take the derivative of both sides with respect to x.
of both sides? why?
Equality only holds if you do to one side what you do to the other. This holds true for differentiation as well
so I get: 1+ln(x)=-2xf(x^2)
I sub in 4 and solve for f(x) right?
Yes, that's what I am getting as well. I then note that f(x^2) = f(4) if x=2. So I would substitute in x=2 to find f(4)...
I get: |dw:1353114453992:dw|
Yep, looks correct to me. If we wanted f(x) in general, we'd probably just substitute in \(x = \sqrt{u}\) so the x^2 inside f(x^2) cancels with the root, but it seems easier to just go directly from f(x^2). :)
Thanks a lot for helping me!
You're welcome! :)

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