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From: Vladimir Bondarenko on 4 Aug 2010 22:20
NIntegrate[
1/Sqrt[(Cos[z] + Cos[2 z] + Cos[3 z] + Cos[4 z])^2 +
(Sin[z] + Sin[2 z] + Sin[3 z] + Sin[4 z])^2],
{z, 0, Pi/2}]

->

13.2482

and no warning is given.

This integral, obviously, diverges.

Maple 14 handles this OK.

evalf(Int(
1/sqrt((cos(z)+cos(2*z)+cos(3*z)+cos(4*z))^2+
(sin(z)+sin(2*z)+sin(3*z)+sin(4*z))^2),
z= 0..Pi/2));

Float(infinity)

Cheers,

Vladimir Bondarenko

Co-founder, CEO, Mathematical Director

http://www.cybertester.com/ Cyber Tester Ltd.

------------------------------------------------------

"We must understand that technologies
like these are the way of the future."

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From: John Smith on 5 Aug 2010 13:23
On Wed, 04 Aug 2010 19:20:25 -0700, Vladimir Bondarenko wrote:

> NIntegrate[
> 1/Sqrt[(Cos[z] + Cos[2 z] + Cos[3 z] + Cos[4 z])^2 +
> (Sin[z] + Sin[2 z] + Sin[3 z] + Sin[4 z])^2],
> {z, 0, Pi/2}]
>
> ->
>
> 13.2482
>
> and no warning is given.
>
> This integral, obviously, diverges.

Maxima handles this integral correctly.

maxima 5.20.1:

i1:1/sqrt((cos(z) + cos(2*z) + cos(3*z) + cos(4*z))^2 +
(sin(z) + sin(2*z) + sin(3*z) + sin(4*z))^2);

quad_qag(i1,z,0,%pi/2,6);
***MESSAGE FROM ROUTINE DQAG IN LIBRARY SLATEC.
***INFORMATIVE MESSAGE, PROG CONTINUES, TRACEBACK REQUESTED
* ABNORMAL RETURN
* ERROR NUMBER = 3
*
***END OF MESSAGE
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