magidin@[EMAIL PROTECTED]
(Arturo Magidin) wrote:
> In article
> <b7abb054-6631-4a8c-bac7-155cfd867e57@[EMAIL PROTECTED]
>,
> J.Agustin <calero565@[EMAIL PROTECTED]
> wrote:
> >Find f(x)=int(1/(1+(sint)^2) , t=a , t=x)
Opening parenthesis ^ inserted.
> I could have sworn I already passed my Calc II course; why are you
> assigning me homework from that course?
>
> Perhaps you meant to ASK for help? Then you shouldn't type your humble
> requests as orders.
>
> But since you ask so nicely, it happens to be Integral number 342
> (with a=b=c=1) in the Table of Indefinite Integrals of the CRC
> Standard Mathematical Tables and Formulae, 31st Edition.
That doesn't help much. That result is the same as what one gets from
Weierstrass substitution, namely, an antiderivative which is not valid on
the whole real line.
The _definite_ integral desired is obviously defined for _all_ real x.
What really puzzles me is why J.Agustin posted his question again here!
Presumably his question has already been thoroughly answered in his recent
sci.math thread "integral". (See the responses there by Slavek and me.)
David
> Alternatively, you can use Weierstrass subsitution,
>
> u = tan(t/2)
>
> to get that sin(t) = 2u/(1+u^2)
> cos(t) = (1-u^2)/(1+u^2)
>
> and transform your integral into the integral of a rational function
> of u, which can then be solved by partial fractions.
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