Trying to find the length of a curve
gx = x^3 - 9 x;
in the interval 0<=x<=3
Wondering why Mathematica produces the following different results:
gx = x^3 - 9 x;
Plot[gx, {x, 0, 3}]
Integrate[Sqrt[1 + (D[gx, x])^2], {x, 0, 3}] // N
NIntegrate[Sqrt[1 + (D[gx, x])^2], {x, 0, 3}]
-0.0633531 + 0.150976 I
21.1806
In addition, if you use the version 10 or higher, you can use the new ArcLength command:
ArcLength[{x, x^3 - 9 x}, {x, 0, 3.0}]
for easier input, and works in all dimensions and can also work in different coordinate systems.
I can also not recreate your complex output (version 10.3 on OSX El Capitan).
Thanks for the reply
$Version
"10.0 for Linux x86 (64-bit) (June 29, 2014)"
I also tried it on a x64 ver 9 Mathematica under Win 7 x64 with the same results
/don’t remember the exact ver and have no access to that machine at the moment/
Have you tried running the 4 lines on a fresh new kernel? If that still gives you the complex result, you should consider sending a bug report.
As a habit anytime I start getting unexpected results I completely shutdown Mathematica and start a fresh session
Quite often the culprit turns out to be some leftover variables from previous computations
This is not the case here though. As for the bug report - I kinda know what the response is going to be - “Update to the latest version”
Thanks for you input once again