# Mathematical Theory - Integral [closed]

Consider this integral

f[g_,b_]=NIntegrate[1/Sqrt[r+g+b],{r,0,Infinity}];

I have to get a value for b , and this value i get when f[g,b]==0 ( or the minimum positive value close to zero ) ( for any g ]

So i was thinking in somethink like this

bvalue[g_]:=Solve[f[g,b]==0,b]

But it dont works , Solve was unable to do that, the program ask me to view a Reduce command. Any ideias how can i do it ?

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## closed as unclear what you're asking by Yves Klett, ssch, Sjoerd C. de Vries, belisarius, rm -rf♦Sep 11 '13 at 15:24

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Assuming g and b are constants you will never get f[g,b]==0 since the integrand is always positive –  ssch Sep 3 '13 at 21:51
@ssch , but i can have f[g,b]-> 0 ( or a minimum value close do zero ) ? –  Lucas G Leite F Pollito Sep 3 '13 at 21:54
@ssch i post a question namely condition for angle integral be 0 ... just like this, but more difiicult expression, and it dont have an analytical solution like here .. can you read that ? –  Lucas G Leite F Pollito Sep 3 '13 at 22:42
In that case I suggest you have a look at FindRoot, FindMinimum and NMinimize –  ssch Sep 3 '13 at 22:56
@ssch , in the opposite case, when f[g,b]->Infinity , the condition is b+r+g == 0 ? –  Lucas G Leite F Pollito Sep 3 '13 at 23:04

It is not possible. Your integral can be written as (with c = r+b)

Integrate[1/Sqrt[c + x], {x, 0, n}, Assumptions -> n > 0]
(* 2 (-Sqrt[c] + Sqrt[n + c]) *)

where $n \rightarrow \infty$

But as we know Sqrt grows unboundedly, so the integral will diverge for all input.

Limit[2 (-Sqrt[c] + Sqrt[n + c]), n -> Infinity]
(* Infinity *)
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but where is the condition for the integral be zero ? i dont understand what you did .. only for b=Infinity the integral will be zero ? –  Lucas G Leite F Pollito Sep 3 '13 at 22:37