Trigonometric integration

[msandeep92]

Hi,

I am solving a big integration, and am struck up in one of the parts ending up as:

∫dx/√(1-k*sin²x)

I have done the following:

I tried with substitution √k*sinx = t;

But it ends up with ∫dt/√[(1 - t²/k)*(1 - t²)]

I dont know how to go ahead with this.

I tried with ksin²x = t also. But that too doesnt work.


Thank you,

Sandeep.

 

[Deleted member 4993]

Hi,

I am solving a big integration, and am struck up in one of the parts ending up as:

∫dx/√(1-k*sin²x)

I have done the following:

I tried with substitution √k*sinx = t;

But it ends up with ∫dt/√[(1 - t²/k)*(1 - t²)]

I dont know how to go ahead with this.

I tried with ksin²x = t also. But that too doesnt work.


Thank you,

Sandeep.

That is an elliptic integral of first kind - cannot be solved in closed form without limits.

A summation solution would be:

f(x) = x + (k x^3)/6 + 1/120 k (-4+9 k) x^5 + O(x⁶)

Use Google to learn more about elliptic functions and their solutions.