2006-08-22 02:59:55 · 6 answers · asked by sanu 2 in Science & Mathematics ➔ Mathematics
Both of the above answers are wrong: dude's answer yields (sin x)/2, not (sin x)^(1/2), and stopwatch's answer gives (sin x)^(1/2) * cos x.
In fact, the reason why you're having so much trouble finding a closed-form antiderivative is because there isn't one. Seriously, √sin x is like e^(x²) - you can integrate it numerically, but there is no simple expression for its integral.
Edit: piyush v, try differentiating the function you just gave us. It doesn't give √(sin x). And anyone else who is thinking of giving a "solution": please double-check your answers before embarrassing yourself.
2006-08-22 04:19:36 · answer #1 · answered by Pascal 7 · 1⤊ 0⤋
This integral cannot be evaluated in terms of elementary
functions. The substitution u = sin x and a bit of
manipulation can reduce it to an integral of a beta
function B(1/4, 1/2). A theorem of Liouville then
tells us that the integral is not elementary.
(The sum of the arguments is not an integer.)
2006-08-25 15:43:29 · answer #2 · answered by steiner1745 7 · 0⤊ 0⤋
according to mr wolfram, and he should know, the integral of Sqrt[Sin[x]] is an elliptic integral of the 2nd kind. Goto the url below to check it out for yourself, (but be careful of your syntax when entering the integral!!!) :--
2006-08-22 06:03:17 · answer #3 · answered by waif 4 · 0⤊ 1⤋
integration of (sinx)^1/2 is
-2/3{(sinx)^3/2}*cosx
2006-08-22 04:40:38 · answer #4 · answered by piyush v 2 · 0⤊ 2⤋
(-2/3)cosx^(3/2) + const.
2006-08-22 03:05:56 · answer #5 · answered by Stopwatch 2 · 0⤊ 3⤋
-1/2*(cos(x))+constant.
2006-08-22 03:05:55 · answer #6 · answered by Anonymous · 0⤊ 3⤋