Trouble calculating line integral using Green's theorem, complicated integral.
$begingroup$
"Calculate line integral of scalar function [$y(e^x) -1]dx + [e^x]dy$ over curve $C$, where $C$ is the semicircle through $(0, 10), (10, 0)$, and $(0, 10)$"
I plan on using Green's theorem, and since curve C does not include the bottom line on x axis, subtract line integral over this line on x axis from result of area integral from Green's theorem. However, I am having trouble calculating the line integral over this bottom curve, I've tried using cartesian and polar coordinates, but it gets very complex. Am I doing something wrong?
greens-theorem
edited Dec 2 '18 at 12:32
amWhy
192k28225439
asked Dec 2 '18 at 12:26
MinYoung KimMinYoung Kim
82
$endgroup$
add a comment |
$begingroup$
"Calculate line integral of scalar function [$y(e^x) -1]dx + [e^x]dy$ over curve $C$, where $C$ is the semicircle through $(0, 10), (10, 0)$, and $(0, 10)$"
I plan on using Green's theorem, and since curve C does not include the bottom line on x axis, subtract line integral over this line on x axis from result of area integral from Green's theorem. However, I am having trouble calculating the line integral over this bottom curve, I've tried using cartesian and polar coordinates, but it gets very complex. Am I doing something wrong?
greens-theorem
edited Dec 2 '18 at 12:32
amWhy
192k28225439
asked Dec 2 '18 at 12:26
MinYoung KimMinYoung Kim
82
$endgroup$
$begingroup$
is it y(e^x) (y a function of e^x) or ye^x?
$endgroup$
– Picaud Vincent
Dec 2 '18 at 13:16
$begingroup$
the latter, y * e^x
$endgroup$
– MinYoung Kim
Dec 3 '18 at 8:23
add a comment |
$begingroup$
"Calculate line integral of scalar function [$y(e^x) -1]dx + [e^x]dy$ over curve $C$, where $C$ is the semicircle through $(0, 10), (10, 0)$, and $(0, 10)$"
I plan on using Green's theorem, and since curve C does not include the bottom line on x axis, subtract line integral over this line on x axis from result of area integral from Green's theorem. However, I am having trouble calculating the line integral over this bottom curve, I've tried using cartesian and polar coordinates, but it gets very complex. Am I doing something wrong?
greens-theorem
edited Dec 2 '18 at 12:32
amWhy
192k28225439
asked Dec 2 '18 at 12:26
MinYoung KimMinYoung Kim
82
$endgroup$
"Calculate line integral of scalar function [$y(e^x) -1]dx + [e^x]dy$ over curve $C$, where $C$ is the semicircle through $(0, 10), (10, 0)$, and $(0, 10)$"
I plan on using Green's theorem, and since curve C does not include the bottom line on x axis, subtract line integral over this line on x axis from result of area integral from Green's theorem. However, I am having trouble calculating the line integral over this bottom curve, I've tried using cartesian and polar coordinates, but it gets very complex. Am I doing something wrong?
greens-theorem
greens-theorem
edited Dec 2 '18 at 12:32
amWhy
192k28225439
asked Dec 2 '18 at 12:26
MinYoung KimMinYoung Kim
82
edited Dec 2 '18 at 12:32
amWhy
192k28225439
asked Dec 2 '18 at 12:26
MinYoung KimMinYoung Kim
82
edited Dec 2 '18 at 12:32
amWhy
192k28225439
edited Dec 2 '18 at 12:32
amWhy
192k28225439
edited Dec 2 '18 at 12:32
amWhy
192k28225439
192k28225439
asked Dec 2 '18 at 12:26
MinYoung KimMinYoung Kim
82
asked Dec 2 '18 at 12:26
MinYoung KimMinYoung Kim
82
asked Dec 2 '18 at 12:26
MinYoung KimMinYoung Kim
82
82
$begingroup$
is it y(e^x) (y a function of e^x) or ye^x?
$endgroup$
– Picaud Vincent
Dec 2 '18 at 13:16
$begingroup$
the latter, y * e^x
$endgroup$
– MinYoung Kim
Dec 3 '18 at 8:23
add a comment |
$begingroup$
is it y(e^x) (y a function of e^x) or ye^x?
$endgroup$
– Picaud Vincent
Dec 2 '18 at 13:16
$begingroup$
the latter, y * e^x
$endgroup$
– MinYoung Kim
Dec 3 '18 at 8:23
$begingroup$
is it y(e^x) (y a function of e^x) or ye^x?
$endgroup$
– Picaud Vincent
Dec 2 '18 at 13:16
$begingroup$
is it y(e^x) (y a function of e^x) or ye^x?
$endgroup$
– Picaud Vincent
Dec 2 '18 at 13:16
$begingroup$
the latter, y * e^x
$endgroup$
– MinYoung Kim
Dec 3 '18 at 8:23
$begingroup$
the latter, y * e^x
$endgroup$
– MinYoung Kim
Dec 3 '18 at 8:23
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Green's theorem states that: wiki
"for a curve C positively oriented, piecewise smooth, simple closed in a plane, and D be the region bounded by C. If L and M are functions of (x, y) defined on an open region containing D and have continuous partial derivatives", then:
$$
oint_C Ldx+Mdy=intint_D frac{partial M}{partial x}-frac{partial L}{partial y}dxdy
$$
Your example: $L=ye^x-1$, $M=e^x$
Thus:
$$
oint_C Ldx+Mdy=intint_D e^x-e^xdxdy=0
$$
answered Dec 3 '18 at 9:22
Picaud VincentPicaud Vincent
1,33439
$endgroup$
$begingroup$
I got that part, I was asking how to calculate line integral over bottom to subtract from zero because its calculation was complicated, but I figured it out.
$endgroup$
– MinYoung Kim
Dec 3 '18 at 20:57
$begingroup$
@MinYoungKim Ok, I understand, thanks
$endgroup$
– Picaud Vincent
Dec 3 '18 at 21:23
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%2f3022572%2ftrouble-calculating-line-integral-using-greens-theorem-complicated-integral%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
$begingroup$
Green's theorem states that: wiki
"for a curve C positively oriented, piecewise smooth, simple closed in a plane, and D be the region bounded by C. If L and M are functions of (x, y) defined on an open region containing D and have continuous partial derivatives", then:
$$
oint_C Ldx+Mdy=intint_D frac{partial M}{partial x}-frac{partial L}{partial y}dxdy
$$
Your example: $L=ye^x-1$, $M=e^x$
Thus:
$$
oint_C Ldx+Mdy=intint_D e^x-e^xdxdy=0
$$
answered Dec 3 '18 at 9:22
Picaud VincentPicaud Vincent
1,33439
$endgroup$
$begingroup$
I got that part, I was asking how to calculate line integral over bottom to subtract from zero because its calculation was complicated, but I figured it out.
$endgroup$
– MinYoung Kim
Dec 3 '18 at 20:57
$begingroup$
@MinYoungKim Ok, I understand, thanks
$endgroup$
– Picaud Vincent
Dec 3 '18 at 21:23
add a comment |
$begingroup$
Green's theorem states that: wiki
"for a curve C positively oriented, piecewise smooth, simple closed in a plane, and D be the region bounded by C. If L and M are functions of (x, y) defined on an open region containing D and have continuous partial derivatives", then:
$$
oint_C Ldx+Mdy=intint_D frac{partial M}{partial x}-frac{partial L}{partial y}dxdy
$$
Your example: $L=ye^x-1$, $M=e^x$
Thus:
$$
oint_C Ldx+Mdy=intint_D e^x-e^xdxdy=0
$$
answered Dec 3 '18 at 9:22
Picaud VincentPicaud Vincent
1,33439
$endgroup$
$begingroup$
I got that part, I was asking how to calculate line integral over bottom to subtract from zero because its calculation was complicated, but I figured it out.
$endgroup$
– MinYoung Kim
Dec 3 '18 at 20:57
$begingroup$
@MinYoungKim Ok, I understand, thanks
$endgroup$
– Picaud Vincent
Dec 3 '18 at 21:23
add a comment |
$begingroup$
Green's theorem states that: wiki
"for a curve C positively oriented, piecewise smooth, simple closed in a plane, and D be the region bounded by C. If L and M are functions of (x, y) defined on an open region containing D and have continuous partial derivatives", then:
$$
oint_C Ldx+Mdy=intint_D frac{partial M}{partial x}-frac{partial L}{partial y}dxdy
$$
Your example: $L=ye^x-1$, $M=e^x$
Thus:
$$
oint_C Ldx+Mdy=intint_D e^x-e^xdxdy=0
$$
answered Dec 3 '18 at 9:22
Picaud VincentPicaud Vincent
1,33439
$endgroup$
Green's theorem states that: wiki
"for a curve C positively oriented, piecewise smooth, simple closed in a plane, and D be the region bounded by C. If L and M are functions of (x, y) defined on an open region containing D and have continuous partial derivatives", then:
$$
oint_C Ldx+Mdy=intint_D frac{partial M}{partial x}-frac{partial L}{partial y}dxdy
$$
Your example: $L=ye^x-1$, $M=e^x$
Thus:
$$
oint_C Ldx+Mdy=intint_D e^x-e^xdxdy=0
$$
answered Dec 3 '18 at 9:22
Picaud VincentPicaud Vincent
1,33439
answered Dec 3 '18 at 9:22
Picaud VincentPicaud Vincent
1,33439
answered Dec 3 '18 at 9:22
Picaud VincentPicaud Vincent
1,33439
answered Dec 3 '18 at 9:22
Picaud VincentPicaud Vincent
1,33439
1,33439
$begingroup$
I got that part, I was asking how to calculate line integral over bottom to subtract from zero because its calculation was complicated, but I figured it out.
$endgroup$
– MinYoung Kim
Dec 3 '18 at 20:57
$begingroup$
@MinYoungKim Ok, I understand, thanks
$endgroup$
– Picaud Vincent
Dec 3 '18 at 21:23
add a comment |
$begingroup$
I got that part, I was asking how to calculate line integral over bottom to subtract from zero because its calculation was complicated, but I figured it out.
$endgroup$
– MinYoung Kim
Dec 3 '18 at 20:57
$begingroup$
@MinYoungKim Ok, I understand, thanks
$endgroup$
– Picaud Vincent
Dec 3 '18 at 21:23
$begingroup$
I got that part, I was asking how to calculate line integral over bottom to subtract from zero because its calculation was complicated, but I figured it out.
$endgroup$
– MinYoung Kim
Dec 3 '18 at 20:57
$begingroup$
I got that part, I was asking how to calculate line integral over bottom to subtract from zero because its calculation was complicated, but I figured it out.
$endgroup$
– MinYoung Kim
Dec 3 '18 at 20:57
$begingroup$
@MinYoungKim Ok, I understand, thanks
$endgroup$
– Picaud Vincent
Dec 3 '18 at 21:23
$begingroup$
@MinYoungKim Ok, I understand, thanks
$endgroup$
– Picaud Vincent
Dec 3 '18 at 21:23
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%2f3022572%2ftrouble-calculating-line-integral-using-greens-theorem-complicated-integral%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
$begingroup$
is it y(e^x) (y a function of e^x) or ye^x?
$endgroup$
– Picaud Vincent
Dec 2 '18 at 13:16
$begingroup$
the latter, y * e^x
$endgroup$
– MinYoung Kim
Dec 3 '18 at 8:23