<p> hatch, Integrate algo </p>

1cd90089-6e78-484f-9378-89ddabf11cfe 53 4 5 decimal

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Scalar Integral curve . . . 3 equivalent scalar representations

This document is Edu. Introduction to integrate.

For a fast visit, leave integral accuracy 100 [20 sec]. At 10000 [30 min].

Why so long @ 10000 ? ... so many integrators are called in there !

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Algo style definition
may apply elsewhere
in Smath works u F 11 x 2^+ / :

Transit the system, plot/interpolate z Int u F u x - x int :

Indefinite integral
int(2) not found 6179 z z int u F u x - x int :

∫(z) => function symbol from Maple
very convenient => see "solve(s)" below z ∫ u F u x - x int :

x ∫ z ∫ :

X 4 :

X ∫ 0.470588

x F x Int 2 1 sys x F x x int 2 1 sys x F x ∫ X X ∫ + 15 black 1 5 mat 3 1 sys

Double integral curve z z int z Int u x - x int :

x X 0.75 :

x Int2 z z int :

X Int2 3.7647

x Int2 x ∫ x F 3 1 sys

multiple solve regions x ∫ x X - x solve x ∫ x X + x solve 21 mat 0.4514 2.2153 21 mat 2.2153 - 0.4514 - 21 mat 21 mat

Maple companion 11 x 2^+ / x int maple z z int maple 21 mat x atan z 2^2 / 21 mat

Smath 6179 multiple indefinite integrals

type int(f, in blank space, i.e: a math region as you type the comma ....that's what you get => ================================================= copy/paste, in 'f' type again int(f, =================================== =================================== copy/paste, in 'f' type again int(f, Simpler: in the first, repeat f(, in 'f'

f # int

f # int # int

f # int # int # int

<p> hatch, Integrate algo </p>

Erzeugt eine Matrix für die Darstellung vertikaler Linien zwischen den Funktionen f(x) und 
g(x) im Bereich von x1 bis x2 mit 2*n Linien. Generates a matrix for 2*N vertical lines (hatching) 
between functions f(x) and g(x) in x-range from x1 to x2 f g x.1 x.2 N hatch dx x.2 x.1 - N / (: h x.1 x.1 f x.1 x.1 g 22 mat : x x.1 x.2 dx - x.1 dx + range h h x dx 2 / + x dx 2 / + g x dx 2 / + x dx 2 / + f x dx + x dx + f x dx + x dx + g 42 mat stack : for h 41 line :

integrate algo style f a b z ∫ u f u a b int :

user ... publishing style x f x cos : a 0.5 π * - : b 3 : 12 mat x g 0 : (datum ≡ plot x f x f x g a b 20 hatch 21 sys : 41 sys

plot

f a b z ∫ 1.1411