How to find $ iiint_{S} xyz; dx dy dz$ for a given set $S$?
$begingroup$
Define the set
$
S:={(x,y,z)in mathbb R^{3}:-3<z<1,x^{2}+y^{2}=36}
$
Find the integral
$$
iiint_{S} xyz; dx dy dz.
$$
I am struggling with the equality $x^{2}+y^{2}=36$; I have only encountered inequalities until now: $x^{2}+y^{2}leq36$ would be easy, as
$$
int_{-3}^{1}int_{0}^{6}int_{-sqrt{36-y^2}}^{sqrt{36-y^2}}(xyz);dxdydz
$$
(I hope this is correct for the inequality case) But how can I treat equality $x^{2}+y^{2}=36$?
real-analysis integration multivariable-calculus
asked Jan 15 at 0:59
SABOYSABOY
683311
$endgroup$
add a comment |
$begingroup$
Define the set
$
S:={(x,y,z)in mathbb R^{3}:-3<z<1,x^{2}+y^{2}=36}
$
Find the integral
$$
iiint_{S} xyz; dx dy dz.
$$
I am struggling with the equality $x^{2}+y^{2}=36$; I have only encountered inequalities until now: $x^{2}+y^{2}leq36$ would be easy, as
$$
int_{-3}^{1}int_{0}^{6}int_{-sqrt{36-y^2}}^{sqrt{36-y^2}}(xyz);dxdydz
$$
(I hope this is correct for the inequality case) But how can I treat equality $x^{2}+y^{2}=36$?
real-analysis integration multivariable-calculus
asked Jan 15 at 0:59
SABOYSABOY
683311
$endgroup$
1
$begingroup$
$S$ is the sheet that forms a cylinder. What are you struggling with? Its has volume zero. There is probably a typo.
$endgroup$
– Will M.
Jan 15 at 1:02
add a comment |
$begingroup$
Define the set
$
S:={(x,y,z)in mathbb R^{3}:-3<z<1,x^{2}+y^{2}=36}
$
Find the integral
$$
iiint_{S} xyz; dx dy dz.
$$
I am struggling with the equality $x^{2}+y^{2}=36$; I have only encountered inequalities until now: $x^{2}+y^{2}leq36$ would be easy, as
$$
int_{-3}^{1}int_{0}^{6}int_{-sqrt{36-y^2}}^{sqrt{36-y^2}}(xyz);dxdydz
$$
(I hope this is correct for the inequality case) But how can I treat equality $x^{2}+y^{2}=36$?
real-analysis integration multivariable-calculus
asked Jan 15 at 0:59
SABOYSABOY
683311
$endgroup$
Define the set
$
S:={(x,y,z)in mathbb R^{3}:-3<z<1,x^{2}+y^{2}=36}
$
Find the integral
$$
iiint_{S} xyz; dx dy dz.
$$
I am struggling with the equality $x^{2}+y^{2}=36$; I have only encountered inequalities until now: $x^{2}+y^{2}leq36$ would be easy, as
$$
int_{-3}^{1}int_{0}^{6}int_{-sqrt{36-y^2}}^{sqrt{36-y^2}}(xyz);dxdydz
$$
(I hope this is correct for the inequality case) But how can I treat equality $x^{2}+y^{2}=36$?
real-analysis integration multivariable-calculus
real-analysis integration multivariable-calculus
asked Jan 15 at 0:59
SABOYSABOY
683311
asked Jan 15 at 0:59
SABOYSABOY
683311
edited Jan 15 at 2:19
user587192
asked Jan 15 at 0:59
SABOYSABOY
683311
asked Jan 15 at 0:59
SABOYSABOY
683311
asked Jan 15 at 0:59
SABOYSABOY
683311
683311
1
$begingroup$
$S$ is the sheet that forms a cylinder. What are you struggling with? Its has volume zero. There is probably a typo.
$endgroup$
– Will M.
Jan 15 at 1:02
add a comment |
1
$begingroup$
$S$ is the sheet that forms a cylinder. What are you struggling with? Its has volume zero. There is probably a typo.
$endgroup$
– Will M.
Jan 15 at 1:02
1
1
$begingroup$
$S$ is the sheet that forms a cylinder. What are you struggling with? Its has volume zero. There is probably a typo.
$endgroup$
– Will M.
Jan 15 at 1:02
$begingroup$
$S$ is the sheet that forms a cylinder. What are you struggling with? Its has volume zero. There is probably a typo.
$endgroup$
– Will M.
Jan 15 at 1:02
add a comment |
0
active
oldest
votes
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%2f3073949%2fhow-to-find-iiint-s-xyz-dx-dy-dz-for-a-given-set-s%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
0
active
oldest
votes
0
active
oldest
votes
active
oldest
votes
active
oldest
votes
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%2f3073949%2fhow-to-find-iiint-s-xyz-dx-dy-dz-for-a-given-set-s%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
$begingroup$
$S$ is the sheet that forms a cylinder. What are you struggling with? Its has volume zero. There is probably a typo.
$endgroup$
– Will M.
Jan 15 at 1:02