Integration square root sin x dx?

Answer 1

integration square root sin x dx.
=1/2square root sin x *cos x.

Answer 2

So sorry, but this integral is not elementary.
In fact, we can reduce it to an elliptic integral.
To see this, let u = sin x, x = arcsin u,
dx = du/√(1-u²)
Then the integral becomes
∫√(u) du/√(1-u²),
and, rationalising the denominator,
∫ √(u-u³ du/(1-u²)

Since you have the square root of a cubic polynomial
in the integrand, you now have an elliptic integral.
Finally, here is the result from the Wolfram
integrator for the original problem:

-2E(1/4(π-2x) | 2),
where E is an elliptic integral of the second kind.

Answer 3

integration of square root of sin x dx
integration (sin x)^1/2 dx = [{(sin x)^3/2) / (3/2)}* cos x
= [2cos x.sin x.(sin x)^1/2] / 3
= [sin2x.(sin x)^1/2] / 3

Answer 4

root sin x.dx becomes sin x power 1/2
integration sin x power 1/2 using bracket formula is,
1/2. 1/root sin x. cos x!
in words= half into one by root sinx into cosx!

Answer 5

let sinx = t
cos x dx= dt
dx=dt/cosx
= dt / (1-t^2)^1/2
Required: integrate(sinx ^ 1/2 dx)
integrate( [t^1/2 ]/[(1-t^2)^1/2 dt )
sorry ,I cant solve it by this method,
BUT , I can give u the answer directly.

ANSWER: 2/3[ ( sinx)^3/2]/cosx
2/3 * (sinx)^3/2 * secx

Answer 6

Use a double indispensable. the first indispensable calculates the realm lower than the curve. the 2d indispensable calculates the realm you calculated earlier over a span of 360degrees (a rotation). so it will be: indispensable(0,2pi) indispensable (0,3) y dx dtheta, the position y is the equation you've above.

Answer 7

use substitution method
let u = sin x
and rewrite as
as u^(1/2) du
u should be able to do that