Re: Calculus problem
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Re: Calculus problem
The integral of sin(3x^2) certainly exists (every continuous function is
integrable), but is not an elementary function.
It has been proved that the integrals of the functions e^(-x^2), sin(x^2), and
cos(x^2) are not elementary functions. On the other hand, these functions come
up very often in applications, and special names have been created for them.
In particular,
FresnelS(x):=integral(sin(pi*t^2/2),t,0,x);
FresnelC(x):=integral(cos(pi*t^2/2),t,0,x);
Erf(x):=sqrt(2/pi)*integaral(e^(-t^2/2),t,0,x);
All these functions have been tabulated, the same way as sin, cos, log, tan.
With computers and programming calulators, the integrals can be computed
numerically.
Greetings,
Erika
In article <35318FEA.9DF91728@csci.csusb.edu>,
jhanson@csci.csusb.edu wrote:
>
> Thankyou, that's similar to what MathCad has, and I have absolutely no clue
> what "FresnelS" is... I can't even figure out a good way to do it by
> hand... that's why I asked you resourceful fellows.
>
> GARY WARDALL wrote:
>
> > Using Mathematica:
> >
> > (Pi/6)^(1/2)*FresnelS[(6/Pi)^(1/2)*x]
> >
> > Good Luck
> >
> > Gary Wardall
> >
> > > Someone please integrate this by hand: sin(3x^2)
> > > Then please integrate it using TI-92, then use something like
> > >MathCad or whatever program you may have. Respond with the answers to
> > >me please.
> > > Thankyou.
> > >--
> > >Don't forget to visit http://web.csusb.edu/public/csci/jhanson
>
> --
> Don't forget to visit http://web.csusb.edu/public/csci/jhanson
>
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