Convergence/Divergence of Improper Integrals
$begingroup$
We're asked to investigate whether this improper integral is (absolutely) convergent or divergent.
begin{equation}
int_{0}^{infty}frac{x}{x^3+1} , , mathbb{d}x
end{equation}
I've earlier worked on functions with logarithms and square roots that made it quite easy to use the Comparison Lemma or the Limit Criterion to go any further. But I think this expression needs to first be decomposed before I can operate on it and I can't seem to figure out how. Any hints/help would be appreciated
calculus analysis convergence improper-integrals divergence
asked 1 hour ago
kareem bokaikareem bokai
444
$endgroup$
add a comment |
$begingroup$
We're asked to investigate whether this improper integral is (absolutely) convergent or divergent.
begin{equation}
int_{0}^{infty}frac{x}{x^3+1} , , mathbb{d}x
end{equation}
I've earlier worked on functions with logarithms and square roots that made it quite easy to use the Comparison Lemma or the Limit Criterion to go any further. But I think this expression needs to first be decomposed before I can operate on it and I can't seem to figure out how. Any hints/help would be appreciated
calculus analysis convergence improper-integrals divergence
asked 1 hour ago
kareem bokaikareem bokai
444
$endgroup$
add a comment |
$begingroup$
We're asked to investigate whether this improper integral is (absolutely) convergent or divergent.
begin{equation}
int_{0}^{infty}frac{x}{x^3+1} , , mathbb{d}x
end{equation}
I've earlier worked on functions with logarithms and square roots that made it quite easy to use the Comparison Lemma or the Limit Criterion to go any further. But I think this expression needs to first be decomposed before I can operate on it and I can't seem to figure out how. Any hints/help would be appreciated
calculus analysis convergence improper-integrals divergence
asked 1 hour ago
kareem bokaikareem bokai
444
$endgroup$
We're asked to investigate whether this improper integral is (absolutely) convergent or divergent.
begin{equation}
int_{0}^{infty}frac{x}{x^3+1} , , mathbb{d}x
end{equation}
I've earlier worked on functions with logarithms and square roots that made it quite easy to use the Comparison Lemma or the Limit Criterion to go any further. But I think this expression needs to first be decomposed before I can operate on it and I can't seem to figure out how. Any hints/help would be appreciated
calculus analysis convergence improper-integrals divergence
calculus analysis convergence improper-integrals divergence
asked 1 hour ago
kareem bokaikareem bokai
444
asked 1 hour ago
kareem bokaikareem bokai
444
asked 1 hour ago
kareem bokaikareem bokai
444
asked 1 hour ago
kareem bokaikareem bokai
444
asked 1 hour ago
kareem bokaikareem bokai
444
444
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Hint
$$frac{x}{x^3color{red}{+1}} le frac{x}{x^3}=frac{1}{x^2}$$
answered 1 hour ago
StackTDStackTD
22.6k2049
$endgroup$
2
$begingroup$
Alright time to smash this keyboard. I've been trying to decompose this thing for the past couple hours and I didn't realize I could compare it in that sense. Damn. Thanks
$endgroup$
– kareem bokai
1 hour ago
$begingroup$
No smashing, please! You're welcome :).
$endgroup$
– StackTD
1 hour ago
add a comment |
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
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: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
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
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
var $window = $(window),
onScroll = function(e) {
var $elem = $('.new-login-left'),
docViewTop = $window.scrollTop(),
docViewBottom = docViewTop + $window.height(),
elemTop = $elem.offset().top,
elemBottom = elemTop + $elem.height();
if ((docViewTop elemBottom)) {
StackExchange.using('gps', function() { StackExchange.gps.track('embedded_signup_form.view', { location: 'question_page' }); });
$window.unbind('scroll', onScroll);
}
};
$window.on('scroll', onScroll);
});
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%2fmath.stackexchange.com%2fquestions%2f3075818%2fconvergence-divergence-of-improper-integrals%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Hint
$$frac{x}{x^3color{red}{+1}} le frac{x}{x^3}=frac{1}{x^2}$$
answered 1 hour ago
StackTDStackTD
22.6k2049
$endgroup$
2
$begingroup$
Alright time to smash this keyboard. I've been trying to decompose this thing for the past couple hours and I didn't realize I could compare it in that sense. Damn. Thanks
$endgroup$
– kareem bokai
1 hour ago
$begingroup$
No smashing, please! You're welcome :).
$endgroup$
– StackTD
1 hour ago
add a comment |
$begingroup$
Hint
$$frac{x}{x^3color{red}{+1}} le frac{x}{x^3}=frac{1}{x^2}$$
answered 1 hour ago
StackTDStackTD
22.6k2049
$endgroup$
2
$begingroup$
Alright time to smash this keyboard. I've been trying to decompose this thing for the past couple hours and I didn't realize I could compare it in that sense. Damn. Thanks
$endgroup$
– kareem bokai
1 hour ago
$begingroup$
No smashing, please! You're welcome :).
$endgroup$
– StackTD
1 hour ago
add a comment |
$begingroup$
Hint
$$frac{x}{x^3color{red}{+1}} le frac{x}{x^3}=frac{1}{x^2}$$
answered 1 hour ago
StackTDStackTD
22.6k2049
$endgroup$
Hint
$$frac{x}{x^3color{red}{+1}} le frac{x}{x^3}=frac{1}{x^2}$$
answered 1 hour ago
StackTDStackTD
22.6k2049
answered 1 hour ago
StackTDStackTD
22.6k2049
answered 1 hour ago
StackTDStackTD
22.6k2049
answered 1 hour ago
StackTDStackTD
22.6k2049
22.6k2049
2
$begingroup$
Alright time to smash this keyboard. I've been trying to decompose this thing for the past couple hours and I didn't realize I could compare it in that sense. Damn. Thanks
$endgroup$
– kareem bokai
1 hour ago
$begingroup$
No smashing, please! You're welcome :).
$endgroup$
– StackTD
1 hour ago
add a comment |
2
$begingroup$
Alright time to smash this keyboard. I've been trying to decompose this thing for the past couple hours and I didn't realize I could compare it in that sense. Damn. Thanks
$endgroup$
– kareem bokai
1 hour ago
$begingroup$
No smashing, please! You're welcome :).
$endgroup$
– StackTD
1 hour ago
2
2
$begingroup$
Alright time to smash this keyboard. I've been trying to decompose this thing for the past couple hours and I didn't realize I could compare it in that sense. Damn. Thanks
$endgroup$
– kareem bokai
1 hour ago
$begingroup$
Alright time to smash this keyboard. I've been trying to decompose this thing for the past couple hours and I didn't realize I could compare it in that sense. Damn. Thanks
$endgroup$
– kareem bokai
1 hour ago
$begingroup$
No smashing, please! You're welcome :).
$endgroup$
– StackTD
1 hour ago
$begingroup$
No smashing, please! You're welcome :).
$endgroup$
– StackTD
1 hour ago
add a comment |
Thanks for contributing an answer to Mathematics 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');
var $window = $(window),
onScroll = function(e) {
var $elem = $('.new-login-left'),
docViewTop = $window.scrollTop(),
docViewBottom = docViewTop + $window.height(),
elemTop = $elem.offset().top,
elemBottom = elemTop + $elem.height();
if ((docViewTop elemBottom)) {
StackExchange.using('gps', function() { StackExchange.gps.track('embedded_signup_form.view', { location: 'question_page' }); });
$window.unbind('scroll', onScroll);
}
};
$window.on('scroll', onScroll);
});
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%2fmath.stackexchange.com%2fquestions%2f3075818%2fconvergence-divergence-of-improper-integrals%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');
var $window = $(window),
onScroll = function(e) {
var $elem = $('.new-login-left'),
docViewTop = $window.scrollTop(),
docViewBottom = docViewTop + $window.height(),
elemTop = $elem.offset().top,
elemBottom = elemTop + $elem.height();
if ((docViewTop elemBottom)) {
StackExchange.using('gps', function() { StackExchange.gps.track('embedded_signup_form.view', { location: 'question_page' }); });
$window.unbind('scroll', onScroll);
}
};
$window.on('scroll', onScroll);
});
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');
var $window = $(window),
onScroll = function(e) {
var $elem = $('.new-login-left'),
docViewTop = $window.scrollTop(),
docViewBottom = docViewTop + $window.height(),
elemTop = $elem.offset().top,
elemBottom = elemTop + $elem.height();
if ((docViewTop elemBottom)) {
StackExchange.using('gps', function() { StackExchange.gps.track('embedded_signup_form.view', { location: 'question_page' }); });
$window.unbind('scroll', onScroll);
}
};
$window.on('scroll', onScroll);
});
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');
var $window = $(window),
onScroll = function(e) {
var $elem = $('.new-login-left'),
docViewTop = $window.scrollTop(),
docViewBottom = docViewTop + $window.height(),
elemTop = $elem.offset().top,
elemBottom = elemTop + $elem.height();
if ((docViewTop elemBottom)) {
StackExchange.using('gps', function() { StackExchange.gps.track('embedded_signup_form.view', { location: 'question_page' }); });
$window.unbind('scroll', onScroll);
}
};
$window.on('scroll', onScroll);
});
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
