Evaluate $intint_Ge^yover x+ydxdy$evaluating this difficult integralSurface Integral over a Vector Field questionEvaluate$int_-2^2int_y^2-3^5-y^2dxdy$Evaluate $int_-2^2int_y^2-3^5-y^2dxdy$Explain why you could have have predicted the result… By inspection: $int^2_0 int^4-x^2_0 x^3 dydx = frac163 units^3 $Evaluate the double integral boundedEvaluate the double integral $intint_R(x^2-2y) $ $dxdy$Changing integration order of $int_0^1int_e^y-1^e^y f(x,y)dxdy$$iint f(x)g(y)dxdy =int f(x)dx int g(y)dy $ Why?finding area using double integrals
How to manage monthly salary
How can I add custom success page
I’m planning on buying a laser printer but concerned about the life cycle of toner in the machine
What is the offset in a seaplane's hull?
Set up public ip on server
Does the average primeness of natural numbers tend to zero?
Is every set a filtered colimit of finite sets?
How to answer pointed "are you quitting" questioning when I don't want them to suspect
How to move the player while also allowing forces to affect it
Calculate Levenshtein distance between two strings in Python
Is it legal to have the "// (c) 2019 John Smith" header in all files when there are hundreds of contributors?
LM317 - Calculate dissipation due to voltage drop
Is this food a bread or a loaf?
What are the advantages and disadvantages of running one shots compared to campaigns?
Could a US political party gain complete control over the government by removing checks & balances?
Why do UK politicians seemingly ignore opinion polls on Brexit?
How to handle columns with categorical data and many unique values
Symmetry in quantum mechanics
Is there a familial term for apples and pears?
Is this homebrew feat, Beast of Burden, balanced?
Why was the "bread communication" in the arena of Catching Fire left out in the movie?
What is GPS' 19 year rollover and does it present a cybersecurity issue?
Domain expired, GoDaddy holds it and is asking more money
Is domain driven design an anti-SQL pattern?
Evaluate $intint_Ge^yover x+ydxdy$
evaluating this difficult integralSurface Integral over a Vector Field questionEvaluate$int_-2^2int_y^2-3^5-y^2dxdy$Evaluate $int_-2^2int_y^2-3^5-y^2dxdy$Explain why you could have have predicted the result… By inspection: $int^2_0 int^4-x^2_0 x^3 dydx = frac163 units^3 $Evaluate the double integral boundedEvaluate the double integral $intint_R(x^2-2y) $ $dxdy$Changing integration order of $int_0^1int_e^y-1^e^y f(x,y)dxdy$$iint f(x)g(y)dxdy =int f(x)dx int g(y)dy $ Why?finding area using double integrals
$begingroup$
Evaluate $intint_Ge^yover x+ydxdy$ where G is the triangle enclosed by $x+y=1$, x axis and y axis.
My attempt:
let $u=x+y$, $v=y$, $|J|=1$
$$int_0^1int_0^-x+1e^yover x+ydydx=int_0^1int_0^1e^vover udvdu$$
But still I couldn't figure out this.
calculus
asked Jan 27 at 18:40
Yibei HeYibei He
3139
$endgroup$
add a comment |
$begingroup$
Evaluate $intint_Ge^yover x+ydxdy$ where G is the triangle enclosed by $x+y=1$, x axis and y axis.
My attempt:
let $u=x+y$, $v=y$, $|J|=1$
$$int_0^1int_0^-x+1e^yover x+ydydx=int_0^1int_0^1e^vover udvdu$$
But still I couldn't figure out this.
calculus
asked Jan 27 at 18:40
Yibei HeYibei He
3139
$endgroup$
$begingroup$
In this triangle, $u ge v$ so you'd want the $v$ integral to go from $0$ to $u$.
$endgroup$
– Robert Israel
Jan 27 at 18:54
$begingroup$
Yes, I did miss that, thank you!
$endgroup$
– Yibei He
Jan 27 at 19:00
add a comment |
$begingroup$
Evaluate $intint_Ge^yover x+ydxdy$ where G is the triangle enclosed by $x+y=1$, x axis and y axis.
My attempt:
let $u=x+y$, $v=y$, $|J|=1$
$$int_0^1int_0^-x+1e^yover x+ydydx=int_0^1int_0^1e^vover udvdu$$
But still I couldn't figure out this.
calculus
asked Jan 27 at 18:40
Yibei HeYibei He
3139
$endgroup$
Evaluate $intint_Ge^yover x+ydxdy$ where G is the triangle enclosed by $x+y=1$, x axis and y axis.
My attempt:
let $u=x+y$, $v=y$, $|J|=1$
$$int_0^1int_0^-x+1e^yover x+ydydx=int_0^1int_0^1e^vover udvdu$$
But still I couldn't figure out this.
calculus
calculus
asked Jan 27 at 18:40
Yibei HeYibei He
3139
asked Jan 27 at 18:40
Yibei HeYibei He
3139
asked Jan 27 at 18:40
Yibei HeYibei He
3139
asked Jan 27 at 18:40
Yibei HeYibei He
3139
asked Jan 27 at 18:40
Yibei HeYibei He
3139
3139
$begingroup$
In this triangle, $u ge v$ so you'd want the $v$ integral to go from $0$ to $u$.
$endgroup$
– Robert Israel
Jan 27 at 18:54
$begingroup$
Yes, I did miss that, thank you!
$endgroup$
– Yibei He
Jan 27 at 19:00
add a comment |
$begingroup$
In this triangle, $u ge v$ so you'd want the $v$ integral to go from $0$ to $u$.
$endgroup$
– Robert Israel
Jan 27 at 18:54
$begingroup$
Yes, I did miss that, thank you!
$endgroup$
– Yibei He
Jan 27 at 19:00
$begingroup$
In this triangle, $u ge v$ so you'd want the $v$ integral to go from $0$ to $u$.
$endgroup$
– Robert Israel
Jan 27 at 18:54
$begingroup$
In this triangle, $u ge v$ so you'd want the $v$ integral to go from $0$ to $u$.
$endgroup$
– Robert Israel
Jan 27 at 18:54
$begingroup$
Yes, I did miss that, thank you!
$endgroup$
– Yibei He
Jan 27 at 19:00
$begingroup$
Yes, I did miss that, thank you!
$endgroup$
– Yibei He
Jan 27 at 19:00
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Consider the substitution
$$x=rcos^2phi,quad y=rsin^2phi,
$$
with $|J|=rsin2phi $, which results in
$$
intint_Ge^yover x+ydxdy=int_0^1 drint_0^pi/2e^sin^2phirsin2phi; dphi\
stackrelsin^2phimapsto u=int_0^1 rdrint_0^1e^udu=frac e-12.
$$
answered Jan 27 at 20:50
useruser
6,34611031
$endgroup$
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');
);
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%2f3089964%2fevaluate-int-int-gey-over-xydxdy%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
$begingroup$
Consider the substitution
$$x=rcos^2phi,quad y=rsin^2phi,
$$
with $|J|=rsin2phi $, which results in
$$
intint_Ge^yover x+ydxdy=int_0^1 drint_0^pi/2e^sin^2phirsin2phi; dphi\
stackrelsin^2phimapsto u=int_0^1 rdrint_0^1e^udu=frac e-12.
$$
answered Jan 27 at 20:50
useruser
6,34611031
$endgroup$
add a comment |
$begingroup$
Consider the substitution
$$x=rcos^2phi,quad y=rsin^2phi,
$$
with $|J|=rsin2phi $, which results in
$$
intint_Ge^yover x+ydxdy=int_0^1 drint_0^pi/2e^sin^2phirsin2phi; dphi\
stackrelsin^2phimapsto u=int_0^1 rdrint_0^1e^udu=frac e-12.
$$
answered Jan 27 at 20:50
useruser
6,34611031
$endgroup$
add a comment |
$begingroup$
Consider the substitution
$$x=rcos^2phi,quad y=rsin^2phi,
$$
with $|J|=rsin2phi $, which results in
$$
intint_Ge^yover x+ydxdy=int_0^1 drint_0^pi/2e^sin^2phirsin2phi; dphi\
stackrelsin^2phimapsto u=int_0^1 rdrint_0^1e^udu=frac e-12.
$$
answered Jan 27 at 20:50
useruser
6,34611031
$endgroup$
Consider the substitution
$$x=rcos^2phi,quad y=rsin^2phi,
$$
with $|J|=rsin2phi $, which results in
$$
intint_Ge^yover x+ydxdy=int_0^1 drint_0^pi/2e^sin^2phirsin2phi; dphi\
stackrelsin^2phimapsto u=int_0^1 rdrint_0^1e^udu=frac e-12.
$$
answered Jan 27 at 20:50
useruser
6,34611031
edited Mar 30 at 0:21
answered Jan 27 at 20:50
useruser
6,34611031
answered Jan 27 at 20:50
useruser
6,34611031
answered Jan 27 at 20:50
useruser
6,34611031
6,34611031
add a comment |
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');
);
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%2f3089964%2fevaluate-int-int-gey-over-xydxdy%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
$begingroup$
In this triangle, $u ge v$ so you'd want the $v$ integral to go from $0$ to $u$.
$endgroup$
– Robert Israel
Jan 27 at 18:54
$begingroup$
Yes, I did miss that, thank you!
$endgroup$
– Yibei He
Jan 27 at 19:00