98fb20a6-8368-4bfc-aa58-45382c791d0e 10 6 9 decimal

&[DATE] &[TIME] - &[FILENAME]

Exercise with the double integral

x y f x exp 0.5 y 3^- (* 1 - :

x y f (y diff 3 y 2^* x exp * -

Recast the integrand in term 
of 'y' limit wrt 'x' b x Φ 3 x exp * b x - (2^* - :

a 0 : b 1 : 12 mat respective limits ≡

SurfaceArea is in |abs| ...
SurfaceArea can't be negative b b x Φ x a b int + abs 0.309691

Absolute error 0.309691 0.29945 - 0.010241

relative error 1 0.309691 0.29945 / - 0.034199 -

Note: Our yardstick is Mathcad 11, which agrees vs "Simplex" ± 1e-15

1.309716 - b + abs 0.309716

data x 01 0.01 range : i 1 x rows range y i el b x i el Φ : for x y augment 31 line :

data Σ Finite differences Cumul Integration vx data 1 col : vy data 2 col : Y 1 el 0 : i 2 vx rows range Δx i el vx i el vx i 1 - el - : Y i el Y i 1 - el 12 / vy i 1 - el vy i el + (Δx i el * (* + : 21 line for vx Y augment 61 line :

data Σ 101 row 1 1.309716 - 12 mat