; Demo of numerical integration

; a simple one
a = INTEG(SIN(x),x,0,PI)
a_true = 2

; an important improper integral
b = INTEG(EXP(-x^2),x,0,INF)
b_true = SQRT(PI)/2

; an integral with a nasty singularity at an endpoint
c = INTEG(x^-.5 LN(x),x,0,1)
c_true = -4

d = INTEG(|x^2 + 2x - 2|^-.5,x,0,1)
; the nasty singularity is near SQRT(3)-1, so try to remove it
sing = SQRT(3) - 1
d1 = INTEG(|x^2 + 2x - 2|^-.5,x,0,sing) +
     INTEG(|x^2 + 2x - 2|^-.5,x,sing,1)
d_true = PI/2 - ATAN(2^-.5) + LN(3)/2