Re: Calculus problem
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Re: Calculus problem
jhanson <jhanson@CSCI.CSUSB.EDU> wrote:
: Someone please integrate this by hand: sin(3x^2)
I got this formula out of the CRC "Standard Mathematical Tables and
Formulae", 29th Edition. (If you don't have this book, I highly suggest it
for reference.) Please excuse the poor rendition in text-only mode.
- Inf
/ 1
| sin ax^n dx = -------- * GAMMA(1/n) * sin (PI/2n)
/ na^(1/n)
- 0
(This is the definite integral from 0 to Infinity, for n > 1)
Where GAMMA(1) = 1
GAMMA(1/2) = sqrt(PI)
GAMMA(n+1) = n*GAMMA(n) for n > 0
So, we get that the integral of sin(3x^2) as evaluated from 0 to infinity
equals:
1/(2*3^(1/2)) * GAMMA(1/2) * sin(PI/2*2)
= sqrt(PI)/(2*sqrt(3)) * sin(PI/4)
I couldn't find reference to a non-definite (ie. open) integral. Perhaps
it doesn't exist in closed form, but I think you could evaluate the
integral by using parts (even if it is messy).
/------------------------------------------------------------------------\
/ Terry Fleury - tfleury@uiuc.edu - http://www.students.uiuc.edu/~tfleury/ \
\ "Give me the credit (with interest, please)." - Wir /
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References: