Integral of the integral using NIntegrateNIntegrate inside NSumNested Nintegrate - two variable limits of integralNIntegrate giving error NIntegrate::nlimDivergence With NIntegrateEvaluating this double integral numerically using NIntegrateNIntegrate::slwcon, NIntegrate::eincr and Set::wrsym problemsQuestion regarding NIntegrate using the Arg functionNumerical integration gives errors NIntegrate::slwcon: and Integrate::eincr:Integration issue with Nintegrate over finite boundsNIntegrate failed to converge to prescribed accuracy for an Integral function with several singular points
Why is my read in of data taking so long?
How to copy a file transactionally?
Is there a reason why I should not use the HaveIBeenPwned API to warn users about exposed passwords?
powerhouse of ideas
Does the Intel 8086 CPU have user mode and kernel mode?
How do professional electronic musicians/sound engineers combat listening fatigue?
How can I stop myself from micromanaging other PCs' actions?
Are there any examples of technologies have been lost over time?
Is it correct to translate English noun adjuncts into adjectives?
Is it legal for private citizens to "impound" e-scooters?
How can I prevent corporations from growing their own workforce?
How do I run a game when my PCs have different approaches to combat?
Why is chess failing to attract big name sponsors?
Explanation for a joke about a three-legged dog that walks into a bar
Does academia have a lazy work culture?
How do I generate distribution of positive numbers only with min, max and mean?
What does "see" in "the Holy See" mean?
How can I receive packages while in France?
Why are so many countries still in the Commonwealth?
Examples of simultaneous independent breakthroughs
Memory capability and powers of 2
Can the 2019 UA Artificer's Returning Weapon and Radiant Weapon infusions stack on the same weapon?
How do campaign rallies gain candidates votes?
Where to place an artificial gland in the human body?
Integral of the integral using NIntegrate
NIntegrate inside NSumNested Nintegrate - two variable limits of integralNIntegrate giving error NIntegrate::nlimDivergence With NIntegrateEvaluating this double integral numerically using NIntegrateNIntegrate::slwcon, NIntegrate::eincr and Set::wrsym problemsQuestion regarding NIntegrate using the Arg functionNumerical integration gives errors NIntegrate::slwcon: and Integrate::eincr:Integration issue with Nintegrate over finite boundsNIntegrate failed to converge to prescribed accuracy for an Integral function with several singular points
.everyoneloves__top-leaderboard:empty,.everyoneloves__mid-leaderboard:empty,.everyoneloves__bot-mid-leaderboard:empty margin-bottom:0;
$begingroup$
Consider the integral
NIntegrate[Exp[-NIntegrate[x, x, 0, y]], y, 0, 2.8]
It displays an error x = y is not a valid limit of integration, however, gives some number. What is a reason for the error and how to interpret the numeric result?
Of course, I can easily replace the integration symbol in the exponent by the value of the integral, however, this is only a toy example demonstrating the problem.
numerical-integration syntax
edited 8 hours ago
Henrik Schumacher
65.8k5 gold badges94 silver badges182 bronze badges
asked 8 hours ago
John TaylorJohn Taylor
9434 silver badges11 bronze badges
$endgroup$
add a comment |
$begingroup$
Consider the integral
NIntegrate[Exp[-NIntegrate[x, x, 0, y]], y, 0, 2.8]
It displays an error x = y is not a valid limit of integration, however, gives some number. What is a reason for the error and how to interpret the numeric result?
Of course, I can easily replace the integration symbol in the exponent by the value of the integral, however, this is only a toy example demonstrating the problem.
numerical-integration syntax
edited 8 hours ago
Henrik Schumacher
65.8k5 gold badges94 silver badges182 bronze badges
asked 8 hours ago
John TaylorJohn Taylor
9434 silver badges11 bronze badges
$endgroup$
1
$begingroup$
Of course you cannot perform the inner numerical integral with an un-specified (free) variable.
$endgroup$
– David G. Stork
8 hours ago
$begingroup$
@DavidG.Stork : however, it turned out that Mathematica gives the correct answer. Why this is possible?
$endgroup$
– John Taylor
8 hours ago
1
$begingroup$
Hmmm.... a tricky question about the internal methods of Mathematica. Frankly, I don't know why the correct answer is given (despite the error messages).
$endgroup$
– David G. Stork
8 hours ago
2
$begingroup$
Mathematica does not have to evaluate the integrand symbolically, in order to apply numerical quadrature. However, it does so usually in order to analyze the integrand. If it fails, it throws an error and tries purely numerical methods. This why it works in the end.
$endgroup$
– Henrik Schumacher
7 hours ago
add a comment |
$begingroup$
Consider the integral
NIntegrate[Exp[-NIntegrate[x, x, 0, y]], y, 0, 2.8]
It displays an error x = y is not a valid limit of integration, however, gives some number. What is a reason for the error and how to interpret the numeric result?
Of course, I can easily replace the integration symbol in the exponent by the value of the integral, however, this is only a toy example demonstrating the problem.
numerical-integration syntax
edited 8 hours ago
Henrik Schumacher
65.8k5 gold badges94 silver badges182 bronze badges
asked 8 hours ago
John TaylorJohn Taylor
9434 silver badges11 bronze badges
$endgroup$
Consider the integral
NIntegrate[Exp[-NIntegrate[x, x, 0, y]], y, 0, 2.8]
It displays an error x = y is not a valid limit of integration, however, gives some number. What is a reason for the error and how to interpret the numeric result?
Of course, I can easily replace the integration symbol in the exponent by the value of the integral, however, this is only a toy example demonstrating the problem.
numerical-integration syntax
numerical-integration syntax
edited 8 hours ago
Henrik Schumacher
65.8k5 gold badges94 silver badges182 bronze badges
asked 8 hours ago
John TaylorJohn Taylor
9434 silver badges11 bronze badges
edited 8 hours ago
Henrik Schumacher
65.8k5 gold badges94 silver badges182 bronze badges
asked 8 hours ago
John TaylorJohn Taylor
9434 silver badges11 bronze badges
edited 8 hours ago
Henrik Schumacher
65.8k5 gold badges94 silver badges182 bronze badges
edited 8 hours ago
Henrik Schumacher
65.8k5 gold badges94 silver badges182 bronze badges
edited 8 hours ago
Henrik Schumacher
65.8k5 gold badges94 silver badges182 bronze badges
65.8k5 gold badges94 silver badges182 bronze badges
asked 8 hours ago
John TaylorJohn Taylor
9434 silver badges11 bronze badges
asked 8 hours ago
John TaylorJohn Taylor
9434 silver badges11 bronze badges
asked 8 hours ago
John TaylorJohn Taylor
9434 silver badges11 bronze badges
9434 silver badges11 bronze badges
1
$begingroup$
Of course you cannot perform the inner numerical integral with an un-specified (free) variable.
$endgroup$
– David G. Stork
8 hours ago
$begingroup$
@DavidG.Stork : however, it turned out that Mathematica gives the correct answer. Why this is possible?
$endgroup$
– John Taylor
8 hours ago
1
$begingroup$
Hmmm.... a tricky question about the internal methods of Mathematica. Frankly, I don't know why the correct answer is given (despite the error messages).
$endgroup$
– David G. Stork
8 hours ago
2
$begingroup$
Mathematica does not have to evaluate the integrand symbolically, in order to apply numerical quadrature. However, it does so usually in order to analyze the integrand. If it fails, it throws an error and tries purely numerical methods. This why it works in the end.
$endgroup$
– Henrik Schumacher
7 hours ago
add a comment |
1
$begingroup$
Of course you cannot perform the inner numerical integral with an un-specified (free) variable.
$endgroup$
– David G. Stork
8 hours ago
$begingroup$
@DavidG.Stork : however, it turned out that Mathematica gives the correct answer. Why this is possible?
$endgroup$
– John Taylor
8 hours ago
1
$begingroup$
Hmmm.... a tricky question about the internal methods of Mathematica. Frankly, I don't know why the correct answer is given (despite the error messages).
$endgroup$
– David G. Stork
8 hours ago
2
$begingroup$
Mathematica does not have to evaluate the integrand symbolically, in order to apply numerical quadrature. However, it does so usually in order to analyze the integrand. If it fails, it throws an error and tries purely numerical methods. This why it works in the end.
$endgroup$
– Henrik Schumacher
7 hours ago
1
1
$begingroup$
Of course you cannot perform the inner numerical integral with an un-specified (free) variable.
$endgroup$
– David G. Stork
8 hours ago
$begingroup$
Of course you cannot perform the inner numerical integral with an un-specified (free) variable.
$endgroup$
– David G. Stork
8 hours ago
$begingroup$
@DavidG.Stork : however, it turned out that Mathematica gives the correct answer. Why this is possible?
$endgroup$
– John Taylor
8 hours ago
$begingroup$
@DavidG.Stork : however, it turned out that Mathematica gives the correct answer. Why this is possible?
$endgroup$
– John Taylor
8 hours ago
1
1
$begingroup$
Hmmm.... a tricky question about the internal methods of Mathematica. Frankly, I don't know why the correct answer is given (despite the error messages).
$endgroup$
– David G. Stork
8 hours ago
$begingroup$
Hmmm.... a tricky question about the internal methods of Mathematica. Frankly, I don't know why the correct answer is given (despite the error messages).
$endgroup$
– David G. Stork
8 hours ago
2
2
$begingroup$
Mathematica does not have to evaluate the integrand symbolically, in order to apply numerical quadrature. However, it does so usually in order to analyze the integrand. If it fails, it throws an error and tries purely numerical methods. This why it works in the end.
$endgroup$
– Henrik Schumacher
7 hours ago
$begingroup$
Mathematica does not have to evaluate the integrand symbolically, in order to apply numerical quadrature. However, it does so usually in order to analyze the integrand. If it fails, it throws an error and tries purely numerical methods. This why it works in the end.
$endgroup$
– Henrik Schumacher
7 hours ago
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
You may try to restrict the definition of the integrand to avoid symbolic calculation. Like:
f[y_?NumericQ] := Exp[-NIntegrate[x, x, 0, y]];
NIntegrate[f[y], y, 0, 2.8]
answered 8 hours ago
Wen ChernWen Chern
4212 silver badges8 bronze badges
$endgroup$
add a comment |
$begingroup$
Of course you cannot perform the inner numerical integral with an un-specified (free) variable, $y$.
Why not simply perform the analytic integrals and be done with it?
Integrate[Exp[-Integrate[x, x, 0, y]], y, 0, 2.8]
$1.24691$
answered 8 hours ago
David G. StorkDavid G. Stork
25.9k2 gold badges22 silver badges57 bronze badges
$endgroup$
$begingroup$
I have used this simple integral as an example. Realistic integrals I want to use are much more complicated.
$endgroup$
– John Taylor
7 hours ago
add a comment |
Your Answer
StackExchange.ready(function()
var channelOptions =
tags: "".split(" "),
id: "387"
;
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function()
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled)
StackExchange.using("snippets", function()
createEditor();
);
else
createEditor();
);
function createEditor()
StackExchange.prepareEditor(
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: false,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: null,
bindNavPrevention: true,
postfix: "",
imageUploader:
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
,
onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
);
);
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmathematica.stackexchange.com%2fquestions%2f202799%2fintegral-of-the-integral-using-nintegrate%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
You may try to restrict the definition of the integrand to avoid symbolic calculation. Like:
f[y_?NumericQ] := Exp[-NIntegrate[x, x, 0, y]];
NIntegrate[f[y], y, 0, 2.8]
answered 8 hours ago
Wen ChernWen Chern
4212 silver badges8 bronze badges
$endgroup$
add a comment |
$begingroup$
You may try to restrict the definition of the integrand to avoid symbolic calculation. Like:
f[y_?NumericQ] := Exp[-NIntegrate[x, x, 0, y]];
NIntegrate[f[y], y, 0, 2.8]
answered 8 hours ago
Wen ChernWen Chern
4212 silver badges8 bronze badges
$endgroup$
add a comment |
$begingroup$
You may try to restrict the definition of the integrand to avoid symbolic calculation. Like:
f[y_?NumericQ] := Exp[-NIntegrate[x, x, 0, y]];
NIntegrate[f[y], y, 0, 2.8]
answered 8 hours ago
Wen ChernWen Chern
4212 silver badges8 bronze badges
$endgroup$
You may try to restrict the definition of the integrand to avoid symbolic calculation. Like:
f[y_?NumericQ] := Exp[-NIntegrate[x, x, 0, y]];
NIntegrate[f[y], y, 0, 2.8]
answered 8 hours ago
Wen ChernWen Chern
4212 silver badges8 bronze badges
answered 8 hours ago
Wen ChernWen Chern
4212 silver badges8 bronze badges
answered 8 hours ago
Wen ChernWen Chern
4212 silver badges8 bronze badges
answered 8 hours ago
Wen ChernWen Chern
4212 silver badges8 bronze badges
4212 silver badges8 bronze badges
add a comment |
add a comment |
$begingroup$
Of course you cannot perform the inner numerical integral with an un-specified (free) variable, $y$.
Why not simply perform the analytic integrals and be done with it?
Integrate[Exp[-Integrate[x, x, 0, y]], y, 0, 2.8]
$1.24691$
answered 8 hours ago
David G. StorkDavid G. Stork
25.9k2 gold badges22 silver badges57 bronze badges
$endgroup$
$begingroup$
I have used this simple integral as an example. Realistic integrals I want to use are much more complicated.
$endgroup$
– John Taylor
7 hours ago
add a comment |
$begingroup$
Of course you cannot perform the inner numerical integral with an un-specified (free) variable, $y$.
Why not simply perform the analytic integrals and be done with it?
Integrate[Exp[-Integrate[x, x, 0, y]], y, 0, 2.8]
$1.24691$
answered 8 hours ago
David G. StorkDavid G. Stork
25.9k2 gold badges22 silver badges57 bronze badges
$endgroup$
$begingroup$
I have used this simple integral as an example. Realistic integrals I want to use are much more complicated.
$endgroup$
– John Taylor
7 hours ago
add a comment |
$begingroup$
Of course you cannot perform the inner numerical integral with an un-specified (free) variable, $y$.
Why not simply perform the analytic integrals and be done with it?
Integrate[Exp[-Integrate[x, x, 0, y]], y, 0, 2.8]
$1.24691$
answered 8 hours ago
David G. StorkDavid G. Stork
25.9k2 gold badges22 silver badges57 bronze badges
$endgroup$
Of course you cannot perform the inner numerical integral with an un-specified (free) variable, $y$.
Why not simply perform the analytic integrals and be done with it?
Integrate[Exp[-Integrate[x, x, 0, y]], y, 0, 2.8]
$1.24691$
answered 8 hours ago
David G. StorkDavid G. Stork
25.9k2 gold badges22 silver badges57 bronze badges
answered 8 hours ago
David G. StorkDavid G. Stork
25.9k2 gold badges22 silver badges57 bronze badges
answered 8 hours ago
David G. StorkDavid G. Stork
25.9k2 gold badges22 silver badges57 bronze badges
answered 8 hours ago
David G. StorkDavid G. Stork
25.9k2 gold badges22 silver badges57 bronze badges
25.9k2 gold badges22 silver badges57 bronze badges
$begingroup$
I have used this simple integral as an example. Realistic integrals I want to use are much more complicated.
$endgroup$
– John Taylor
7 hours ago
add a comment |
$begingroup$
I have used this simple integral as an example. Realistic integrals I want to use are much more complicated.
$endgroup$
– John Taylor
7 hours ago
$begingroup$
I have used this simple integral as an example. Realistic integrals I want to use are much more complicated.
$endgroup$
– John Taylor
7 hours ago
$begingroup$
I have used this simple integral as an example. Realistic integrals I want to use are much more complicated.
$endgroup$
– John Taylor
7 hours ago
add a comment |
Thanks for contributing an answer to Mathematica Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmathematica.stackexchange.com%2fquestions%2f202799%2fintegral-of-the-integral-using-nintegrate%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
1
$begingroup$
Of course you cannot perform the inner numerical integral with an un-specified (free) variable.
$endgroup$
– David G. Stork
8 hours ago
$begingroup$
@DavidG.Stork : however, it turned out that Mathematica gives the correct answer. Why this is possible?
$endgroup$
– John Taylor
8 hours ago
1
$begingroup$
Hmmm.... a tricky question about the internal methods of Mathematica. Frankly, I don't know why the correct answer is given (despite the error messages).
$endgroup$
– David G. Stork
8 hours ago
2
$begingroup$
Mathematica does not have to evaluate the integrand symbolically, in order to apply numerical quadrature. However, it does so usually in order to analyze the integrand. If it fails, it throws an error and tries purely numerical methods. This why it works in the end.
$endgroup$
– Henrik Schumacher
7 hours ago