>> From: Maple User Group "maple_gr"
On Tue, 3 Dec 2002, Benj FitzPatrick wrote:
| I am trying to numerically integrate a certain
| function, say f(x,y). It turns out that x and y are
| functions of t, so the overall integration is done
| with respect to t. Is there any way to do the
| integration and place constraints on x or y (I want to
| be able to have a max value for x that is used when x
| exceeds the limit).
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Date: Wed, 4 Dec 2002 14:58:14 -0500 (EST)
From: Carl Devore "devore"
To: "maple-list"
Subject: Integration problem
Use `min`. For example,
f:= (x,y)-> x*y:
x:= exp(t):
y:= GAMMA(t):
Int(f(min(1000,x),min(2000,y)), t= 0..100);
evalf(%);
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From: "borisal" (Boris Alekseev)
To: "maple-list"
Date: Thu, 05 Dec 2002 22:24:58 +0300
Subject: Integration problem
To insert a constraint on maximal value M of variable x use just min(x,M).
f:=(x,y)->x+y; x:=t; y:=t^2; int(f(min(x,M),y),t=a..b);
f := (x, y) -> x + y
x := t
2
y := t
/{ 3 2 \
|{ 1/3 b + 1/2 b b <= M|
|{ |
|{ 3 2 |
\{ 1/3 b + b M - 1/2 M M < b /
/{ 3 2 \
|{ - 1/3 a - 1/2 a a <= M|
+ |{ |
|{ 3 2 |
\{ - 1/3 a - a M + 1/2 M M < a /
In general situation with some region D on the plane (x,y) use characteristic function g(x,y) of region D, which is equal 1
within D and 0 otherwise, to form an integrant f(x,y)*g(x,y) with support on D and invoke int(f(x,y)*g(x,y),t=-infinity..infinity)
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From: "Dr Francis J. Wright" "F.J.Wright"
To: "benjfitz"
Subject: Integration problem
Date: Fri, 6 Dec 2002 14:18:32 -0000
Can't you just integrate f(min(x,xmax),y) instead of f(x,y)?
Francis
|
(NAG)
