2006-09-20 23:59:52 · 5 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
2cos^(1/2)[x]F[x/2|2]sec^(1/2)[x]
Where F[x|m]: EllipticF[x, m]: elliptic integral of the first kind
2006-09-21 00:10:25 · answer #1 · answered by Chris C 2 · 1⤊ 0⤋
As some of the other answers have shown, it IS integrable,
but not in terms of elementary functions. Of the
6 trig functions only sqrt(tan x) and sqrt(cot x) are
so integrable.As for your integral, let 's proceed
as follows:
Write sec x = 1/cos x and let u = cos x,
x = arccos u, dx = -1/sqrt(1 - u^2).
Plugging everything back in, we get
-int[ du/ sqrt(u(1-u^2)],
an elliptic integral, since it involves integrating
the square root of a cubic polynomial.
2006-09-21 11:54:37 · answer #2 · answered by steiner1745 7 · 1⤊ 0⤋
no, not possible.
reason: actually integration and differentiation are the reverse process, so,there is not a single function which on differentiation gives square root of secx. therefore we can't integrate this function.
2006-09-21 07:15:17 · answer #3 · answered by imran_e_mohammed 1 · 0⤊ 1⤋
I think it is possible. However, it should be kept in mind that this function exhibits discontinuous behaviour at certain points, meaning that the function is not integrable at those points.
2006-09-21 07:11:33 · answer #4 · answered by alimp_82 1 · 1⤊ 0⤋
It is not possible to integrate using ordinary functions, however by using special functions like elliptic function you have a solution. Kindly refer to special functions books to get more details. You can also refer to http://en.wikipedia.org/wiki/Special_functions and also http://www.integrals.com
2006-09-22 05:47:36 · answer #5 · answered by Anonymous · 0⤊ 0⤋