0
$\begingroup$

I have the following integral that I am trying to evaluate in Mathematica:

$\int \sqrt{\alpha + m g l \cos(q)} dq$. If $\alpha > m g l$, then the result is a complete elliptic integral of the second kind and Mathematica outputs EllipticE[m]. If $\alpha < m g l$, then Mathematica outputs and incomplete elliptic integral of the second kind, i.e. EllipticE[$\phi$,m].

I am trying to obtain a general expression for the integral when $\alpha > m g l$, but Mathematica keeps giving me a conditional expression, even after using the Assumptions command with $\alpha > m g l$ and $\alpha \in$ Reals. Does anyone know what's going on here?

$\endgroup$
  • 1
    $\begingroup$ FullSimplify[Integrate[Sqrt[a + b Cos@q], q], Assumptions -> (a > b > 0)] returns 2 Sqrt[a + b] EllipticE[q/2, (2 b)/(a + b)] $\endgroup$ – Dr. belisarius May 8 '15 at 17:28
1
$\begingroup$

In version 8 the integral is very simply solved without any explicit assuptions:

$Version

(*
Out[6]= "8.0 for Microsoft Windows (64-bit) (October 7, 2011)"
*)

Integrate[Sqrt[a + b Cos[q]], q]

(*
Out[5]= (2 Sqrt[a + b Cos[q]] EllipticE[q/2, (2 b)/(a + b)])/Sqrt[(a +
  b Cos[q])/(a + b)]
*)
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.