# 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 ?

-

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

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question.If this question can be reworded to fit the rules in the help center, please edit the question.

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 *)

-
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