Re: Can I get an analytical solution of this integration?

On Jun 27, 9:21 pm, ellieandrogerxy...@xxxxxxxxxxxxxxxxxxxxxx (Roger
Stafford) wrote:
In article <1182932309.342690.93...@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>, Damayi





<dam...@xxxxxxxxx> wrote:
Dear all
'k' is a given constant value and 'a' is a variable which is from 0 to
2*pi.
f = (1+k*(sin(a))^2)^(1/2);
I tried to use 'int' to get the integration of 'f' ,but failed.

int(f,'a',[0,2*pi])
Warning: Warning, unable to determine if 1/2*pi+pi*_Z16 is between a
and 2*pi; try to use assumptions or set _EnvAllSolutions to true
Warning: Explicit integral could not be found.
In sym.int at 58

ans =

int((1+sin(a)^2)^(1/2),a = a .. 2*pi)

Can you give me how to get a analytic solution?

Any comment or advice will be my pleasure. Thanks

mayi
2007-06-27

-------------------
My intuition tells me this integral leads to an elliptic integral of the
second kind, which would account for your not getting a solution. That
doesn't mean it isn't an analytic function, only that it cannot be
expressed in terms of the usual elementary functions that mathematicians
are accustomed to using. Elliptic integrals can actually be computed in
perfectly acceptable ways.

Roger Stafford- Hide quoted text -

- Show quoted text -

Roger
According to my bible (Abramowitz & Stegun) elliptic integrals of the
2nd kind have a minus sign, not plus, in the integrand.


.

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