Integrating function with /; in its definition
$begingroup$
why
f[x_ /; x>=0]:=x;
Integrate[f[x] ,{x,0,2 Pi}]
return unevaluated? Notice that the above definition of f[x] works OK with other Mathematica functions, such as Plot
Plot[f[x], {x, 0, 2 Pi}]
While the following works with Integrate
f[x_]:=x;
Integrate[f[x] ,{x,0,2 Pi}]
I am using version 11.3 on windows.
calculus-and-analysis function-construction
edited 21 mins ago
J. M. is computer-less♦
97.3k10303463
asked 3 hours ago
NasserNasser
58.1k489206
$endgroup$
add a comment |
$begingroup$
why
f[x_ /; x>=0]:=x;
Integrate[f[x] ,{x,0,2 Pi}]
return unevaluated? Notice that the above definition of f[x] works OK with other Mathematica functions, such as Plot
Plot[f[x], {x, 0, 2 Pi}]
While the following works with Integrate
f[x_]:=x;
Integrate[f[x] ,{x,0,2 Pi}]
I am using version 11.3 on windows.
calculus-and-analysis function-construction
edited 21 mins ago
J. M. is computer-less♦
97.3k10303463
asked 3 hours ago
NasserNasser
58.1k489206
$endgroup$
3
$begingroup$
It's better to use ConditionalExpression, e.g.,Integrate[ConditionalExpression[x, x>0], {x, 0, 2Pi}]
$endgroup$
– Carl Woll
3 hours ago
add a comment |
$begingroup$
why
f[x_ /; x>=0]:=x;
Integrate[f[x] ,{x,0,2 Pi}]
return unevaluated? Notice that the above definition of f[x] works OK with other Mathematica functions, such as Plot
Plot[f[x], {x, 0, 2 Pi}]
While the following works with Integrate
f[x_]:=x;
Integrate[f[x] ,{x,0,2 Pi}]
I am using version 11.3 on windows.
calculus-and-analysis function-construction
edited 21 mins ago
J. M. is computer-less♦
97.3k10303463
asked 3 hours ago
NasserNasser
58.1k489206
$endgroup$
why
f[x_ /; x>=0]:=x;
Integrate[f[x] ,{x,0,2 Pi}]
return unevaluated? Notice that the above definition of f[x] works OK with other Mathematica functions, such as Plot
Plot[f[x], {x, 0, 2 Pi}]
While the following works with Integrate
f[x_]:=x;
Integrate[f[x] ,{x,0,2 Pi}]
I am using version 11.3 on windows.
calculus-and-analysis function-construction
calculus-and-analysis function-construction
edited 21 mins ago
J. M. is computer-less♦
97.3k10303463
asked 3 hours ago
NasserNasser
58.1k489206
edited 21 mins ago
J. M. is computer-less♦
97.3k10303463
asked 3 hours ago
NasserNasser
58.1k489206
edited 21 mins ago
J. M. is computer-less♦
97.3k10303463
edited 21 mins ago
J. M. is computer-less♦
97.3k10303463
edited 21 mins ago
J. M. is computer-less♦
97.3k10303463
97.3k10303463
asked 3 hours ago
NasserNasser
58.1k489206
asked 3 hours ago
NasserNasser
58.1k489206
asked 3 hours ago
NasserNasser
58.1k489206
58.1k489206
3
$begingroup$
It's better to use ConditionalExpression, e.g.,Integrate[ConditionalExpression[x, x>0], {x, 0, 2Pi}]
$endgroup$
– Carl Woll
3 hours ago
add a comment |
3
$begingroup$
It's better to use ConditionalExpression, e.g.,Integrate[ConditionalExpression[x, x>0], {x, 0, 2Pi}]
$endgroup$
– Carl Woll
3 hours ago
3
3
$begingroup$
It's better to use ConditionalExpression, e.g.,
Integrate[ConditionalExpression[x, x>0], {x, 0, 2Pi}]$endgroup$
– Carl Woll
3 hours ago
$begingroup$
It's better to use ConditionalExpression, e.g.,
Integrate[ConditionalExpression[x, x>0], {x, 0, 2Pi}]$endgroup$
– Carl Woll
3 hours ago
add a comment |
1 Answer
1
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$begingroup$
f[x_ /; x>=0]:=x means "if whatever>=0 rewrite f[whatever] as whatever. But that doesn't apply to f[x] when x is a symbol without a numerical value. Thus, f[x] simply remains f[x]. For abstracting the notion of a function with a break like this, use Piecewise or HeavisideTheta: Integrate understands what those mean.
answered 3 hours ago
John DotyJohn Doty
7,32811124
$endgroup$
add a comment |
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1 Answer
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votes
$begingroup$
f[x_ /; x>=0]:=x means "if whatever>=0 rewrite f[whatever] as whatever. But that doesn't apply to f[x] when x is a symbol without a numerical value. Thus, f[x] simply remains f[x]. For abstracting the notion of a function with a break like this, use Piecewise or HeavisideTheta: Integrate understands what those mean.
answered 3 hours ago
John DotyJohn Doty
7,32811124
$endgroup$
add a comment |
$begingroup$
f[x_ /; x>=0]:=x means "if whatever>=0 rewrite f[whatever] as whatever. But that doesn't apply to f[x] when x is a symbol without a numerical value. Thus, f[x] simply remains f[x]. For abstracting the notion of a function with a break like this, use Piecewise or HeavisideTheta: Integrate understands what those mean.
answered 3 hours ago
John DotyJohn Doty
7,32811124
$endgroup$
add a comment |
$begingroup$
f[x_ /; x>=0]:=x means "if whatever>=0 rewrite f[whatever] as whatever. But that doesn't apply to f[x] when x is a symbol without a numerical value. Thus, f[x] simply remains f[x]. For abstracting the notion of a function with a break like this, use Piecewise or HeavisideTheta: Integrate understands what those mean.
answered 3 hours ago
John DotyJohn Doty
7,32811124
$endgroup$
f[x_ /; x>=0]:=x means "if whatever>=0 rewrite f[whatever] as whatever. But that doesn't apply to f[x] when x is a symbol without a numerical value. Thus, f[x] simply remains f[x]. For abstracting the notion of a function with a break like this, use Piecewise or HeavisideTheta: Integrate understands what those mean.
answered 3 hours ago
John DotyJohn Doty
7,32811124
answered 3 hours ago
John DotyJohn Doty
7,32811124
answered 3 hours ago
John DotyJohn Doty
7,32811124
answered 3 hours ago
John DotyJohn Doty
7,32811124
7,32811124
add a comment |
add a comment |
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$begingroup$
It's better to use ConditionalExpression, e.g.,
Integrate[ConditionalExpression[x, x>0], {x, 0, 2Pi}]$endgroup$
– Carl Woll
3 hours ago