LET I= THE INTEGRAL FROM 0 T0 INFINITY FOR THE FUNCTION e^-x^2
then I =THE INTEGRAL FOR e^-y^2
then I^2= DOUBLE INTEGRAL FROM 0 TO INFINITY FROM 0 TO INFINITY FOR e-(x^2+y^2) dx dy
put r^2=X^2+y^2 X=r cos
theta y=r sin theta then I^2 =PI/2