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Question: Problem with elliptic integrals and assuming

Question:Problem with elliptic integrals and assuming

chrisc 111 Maple
integral
April 01 2014
0

Hi there

There seems to be a bug when evaluating elliptic integrals using assuming. Here's an example:

 

INT:=Int(1/sqrt(a*x^3+1),x=0..X);

is our integral for some a. Now evaluate the integral using assuming on X in different ways:

 

INT2:=simplify(value(INT)) assuming X>0, a>0, a<1;

INT3:=simplify(value(INT)) assuming X<0, a>0, a<1;

 

These give analytic solutions which are different. Now plot them both and compare to the numeric solution

 

plot([subs(a=0.1,INT2),subs(a=0.1,INT3),subs(a=0.1,INT)],X=-1..1,colour=[red,green,blue]);

 

I'm finding that the red curve which should work for X>0 is wrong, while the green one which is for X<0 is ok for X either sign. [blue is the correct answer - numerically!]

 

Any ideas?
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