Integration Bug

Posted on 2007-09-14 09:59 By clashton (0)

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Run the following two pieces of code

plot(3*arctan((-1+x)*x/(-2+x))/x, x = 0 .. 1)

int(3*arctan((-1+x)*x/(-2+x))/x, x = 0 .. 1)

There seems to be a bug in "int"

I am using Maple 10.

Maple 10 Integration bug

Comment on 2007-09-14 22:33 from gkokovidis ( Maple Rating 4

700)

Maple 10 gives infinity as an answer. Maple 11 gives the answer below:

3/2*I*dilog((-1+I-3^(1/2)+3^(1/2)*I)/(1+I-3^(1/2)+3^(1/2)*I))-3/2*I*dilog((-1-I+3^(1/2)+3^(1/2)*I)/(1-I+3^(1/2)+3^(1/2)*I))-3/2*I*dilog((1+I+3^(1/2)+3^(1/2)*I)/(-1+I+3^(1/2)+3^(1/2)*I))+3/2*I*dilog((1-I-3^(1/2)+3^(1/2)*I)/(-1-I-3^(1/2)+3^(1/2)*I))

Converted to a float it looks like this:

.9159655938+0.*I

I think you are correct about the bug in Maple 10. It should not be infinity. This seems to have been addressed in Maple 11.

Later edit: In Maple 10 you can get the correct answer if you change your limits from 0..1 to 0..1.0 This forces a non symbolic answer which is correct and much faster to compute.

>int(3*arctan((-1+x)*x/(-2+x))/x, x = 0 .. 1.0);

Regards,
Georgios Kokovidis
Dräger Medical

Integration Bug

Maple 10 Integration bug

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