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Reverse integrals 
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#1
Jan1414, 02:54 PM

P: 343

I need to find a function f(x) such that
[tex]\int_{\infty}^{100+10n} (f(x)) dx = 10.1^n[/tex] for n=1,2,3,4,5,6...∞. How would I go about this? It must be exponential in some way I'm guessing? This is not a homework problem. I don't just want the answer. I want guidance on this type of problem and function, but please from someone with an idea of how to answer this particular case too ... 


#2
Jan1414, 03:12 PM

Sci Advisor
P: 6,027

Replace (100+10n) by a real variable (y). Take the derivative of both sides, this will give you an expression for f(y) if it exists. It will be an exponential.



#3
Jan1414, 05:18 PM

P: 343

Now what? I need to bear the integral limits (∞ to y) in mind... 


#4
Jan1514, 03:20 PM

Sci Advisor
P: 6,027

Reverse integrals
0.1^{n} = 0.1^{(y100)/10} = exp((y100)ln(0.1)/10). Now take the derivatives of both sides to get f(y) = .



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