Basic calculus problem

1. May 4, 2013

eas123

1. The problem statement, all variables and given/known data

See attached.

2. Relevant equations

3. The attempt at a solution

I integrated the equation with respect to x to obtain
∫$\frac{d}{dx}$(x$e^{-x}$$\frac{df}{dx}$)dx+∫n$e^{-x}$fdx= constant
The first term on the left hand side goes to zero as x, df/dx are bounded at 0, infinity. This leaves the expression ∫n$e^{-x}$fdx= constant which is not the one given.

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2. May 4, 2013

tiny-tim

hi eas123!

what happened to m ?

3. May 4, 2013

eas123

Hi. :-)

What do you mean? I don't know how to derive the expression.

4. May 4, 2013

tiny-tim

your expected answer, $\int_0^{\infty} e^{-x}f_n(x)f_m(x) dx = 0$, has an "m" in it

i don't see an "m" in your actual work

5. May 4, 2013

eas123

So where have I gone wrong?

6. May 4, 2013

tiny-tim

i'm completely confused

you seem to be solving a different problem

start with $e^{-x}f_n(x)f_m(x) dx = 0$, and integrate it

7. May 4, 2013

SammyS

Staff Emeritus
The following is an image of the attachment. Please notice that the result you are to prove contains both n and m . That's what tiny-tim is telling you.