2007-03-30 22:01:51 · 6 answers · asked by him_12_pat 1 in Science & Mathematics ➔ Mathematics
Integral ( √[sin(x)] dx )
Unless I'm mistaken, this cannot be solved in terms of elementary functions. Substitution, integration by parts, trigonometric identities, trigonometric substitution, or partial fractions will not work.
2007-03-30 22:07:48 · answer #1 · answered by Puggy 7 · 1⤊ 0⤋
Puggy' s quite correct. This integral cannot be
done in terms of elementary functions.
In fact, we can reduce it to an elliptic integral.
Let' s let u = sin x, x = arcsin u, dx = du/sqrt(1-u^2).
Then we have to integrate
sqrt[ u/1-u^2] du
Now rationalise the denominator
and we have to integrate
sqrt[ u(1-u^2)] du/ (1-u^2).
Since we now have a cubic under the
square root sign, we have an elliptic
integral.
2007-03-31 05:45:59 · answer #2 · answered by steiner1745 7 · 0⤊ 0⤋
integration of under root sin x = -2 under root cos x
2007-03-30 22:51:27 · answer #3 · answered by bach 2 · 1⤊ 2⤋
According to Wolfram, this is an elliptic integral of the second type, which I understand to be integrated numerically. There are lookup tables for the definite integral.
2007-03-30 22:34:39 · answer #4 · answered by Helmut 7 · 1⤊ 1⤋
what do you mean underroot?... sin and cosin i kno that much... but i forget what they are used for
2007-03-30 22:05:44 · answer #5 · answered by sexy sexy 2 · 0⤊ 0⤋
I found the answer on this site
http://integrals.wolfram.com/index.jsp anyway it's very complex!
2007-03-30 22:19:22 · answer #6 · answered by MadScientist 2 · 0⤊ 1⤋