Matematické Fórum

stuart clark · 20. 08. 2013 12:25

$\lim_{n\rightarrow \infty}n^2.\int_{-1}^{0} \frac{\tan^{-1}(nx)}{\sin^{-1}(nx)}dx$

Brano · 20. 08. 2013 23:08

Is this meant as an integral of a complex valued function? Since real valued $\arcsin(u)$ is not defined for $u<-1$ .

stuart clark · 30. 08. 2013 20:16

To ↑ Brano: would you like to explain me full answer,

Thanks

Brano · 31. 08. 2013 12:18 — Editoval Brano (31. 08. 2013 12:19)

I suppose that $\sin^{-1}$ means $\text{arcsin}$ . If you consider it as a real valued function, then its domain is $[-1,1]$ but $nx$ ranges over $[-n,0]$ . Then I see at least 3 disjoint possibilities

1) there is an error in your assignement.
2) there is an error in my supposition that $\sin^{-1}$ means $\text{arcsin}$ .
3) you actually mean pricipal branch of complex valued multifunction $\text{Arcsin}$ .

So you should clarify this.

Matematické Fórum

#1 20. 08. 2013 12:25

Inverse definite integral

#2 20. 08. 2013 23:08

Re: Inverse definite integral

#3 30. 08. 2013 20:16

Re: Inverse definite integral

#4 31. 08. 2013 12:18 — Editoval Brano (31. 08. 2013 12:19)

Re: Inverse definite integral

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