integrate(sqrt(x^2+y^2),x,0,1)$ integrate(%,y,0,1)$

• Subject: integrate(sqrt(x^2+y^2),x,0,1)$ integrate(%,y,0,1)$
• From: Bill Wood
• Date: Sat, 06 Apr 2013 11:06:59 -0500

On Fri, 2013-04-05 at 18:35 -0400, Stavros Macrakis wrote:
   . . .
> Is there a simpler way?

For What It's Worth:

(%i1) display2d:false$

(%i2) qq: integrate(integrate(sqrt(x^2+y^2),x,-1,1),y,-1,1);

(%o2) (4*asinh(1)+4*sqrt(2))/3
(%i3) qq1: logarc(qq);

(%o3) (4*log(sqrt(2)+1)+4*sqrt(2))/3
(%i4) qq2: qq1/4;

(%o4) (4*log(sqrt(2)+1)+4*sqrt(2))/12
(%i5) qq3: factor(qq2);

(%o5) (log(sqrt(2)+1)+sqrt(2))/3

The "gimmick" was to change the limits in (%i2); all the non-trivial
work is already done in (%o3).

-- 
Bill Wood

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