Finding the mass of a region given a density function The Next CEO of Stack OverflowFinding a mass of elipseIntegrals - center of mass of non-uniform density sphereFinding the mass of a cone using triple integralFinding volume of a cone given densityFinding mass of a sphere given density = $1-rho^2$ and radius = 1Centre of Mass of a Constant Density LaminaFinding the center of mass with varying densityFinding mass of enclosed region in first quadrant, change of variablesFinding center of mass of a solid with non-uniform densitymass density volume Integration
How did people program for Consoles with multiple CPUs?
Proper way to express "He disappeared them"
What happened in Rome, when the western empire "fell"?
Would a completely good Muggle be able to use a wand?
How to scale a tikZ image which is within a figure environment
What connection does MS Office have to Netscape Navigator?
How to place nodes around a circle from some initial angle?
Why, when going from special to general relativity, do we just replace partial derivatives with covariant derivatives?
Is it okay to majorly distort historical facts while writing a fiction story?
How do I align (1) and (2)?
Some questions about different axiomatic systems for neighbourhoods
Is micro rebar a better way to reinforce concrete than rebar?
Break Away Valves for Launch
Is there a difference between "Fahrstuhl" and "Aufzug"
Should I tutor a student who I know has cheated on their homework?
If Nick Fury and Coulson already knew about aliens (Kree and Skrull) why did they wait until Thor's appearance to start making weapons?
Does falling count as part of my movement?
Do I need to write [sic] when a number is less than 10 but isn't written out?
How to count occurrences of text in a file?
What was the first Unix version to run on a microcomputer?
INSERT to a table from a database to other (same SQL Server) using Dynamic SQL
Won the lottery - how do I keep the money?
Why isn't the Mueller report being released completely and unredacted?
Why doesn't UK go for the same deal Japan has with EU to resolve Brexit?
Finding the mass of a region given a density function
The Next CEO of Stack OverflowFinding a mass of elipseIntegrals - center of mass of non-uniform density sphereFinding the mass of a cone using triple integralFinding volume of a cone given densityFinding mass of a sphere given density = $1-rho^2$ and radius = 1Centre of Mass of a Constant Density LaminaFinding the center of mass with varying densityFinding mass of enclosed region in first quadrant, change of variablesFinding center of mass of a solid with non-uniform densitymass density volume Integration
$begingroup$
I know that this involves multiple integrals and that density = mass / volume but I'm not sure how to set up the integrand given this information.
integration multivariable-calculus
asked Mar 27 at 18:39
krauser126krauser126
636
$endgroup$
add a comment |
$begingroup$
I know that this involves multiple integrals and that density = mass / volume but I'm not sure how to set up the integrand given this information.
integration multivariable-calculus
asked Mar 27 at 18:39
krauser126krauser126
636
$endgroup$
$begingroup$
You just need to integrate the density over the region.
$endgroup$
– saulspatz
Mar 27 at 18:41
add a comment |
$begingroup$
I know that this involves multiple integrals and that density = mass / volume but I'm not sure how to set up the integrand given this information.
integration multivariable-calculus
asked Mar 27 at 18:39
krauser126krauser126
636
$endgroup$
I know that this involves multiple integrals and that density = mass / volume but I'm not sure how to set up the integrand given this information.
integration multivariable-calculus
integration multivariable-calculus
asked Mar 27 at 18:39
krauser126krauser126
636
asked Mar 27 at 18:39
krauser126krauser126
636
asked Mar 27 at 18:39
krauser126krauser126
636
asked Mar 27 at 18:39
krauser126krauser126
636
asked Mar 27 at 18:39
krauser126krauser126
636
636
$begingroup$
You just need to integrate the density over the region.
$endgroup$
– saulspatz
Mar 27 at 18:41
add a comment |
$begingroup$
You just need to integrate the density over the region.
$endgroup$
– saulspatz
Mar 27 at 18:41
$begingroup$
You just need to integrate the density over the region.
$endgroup$
– saulspatz
Mar 27 at 18:41
$begingroup$
You just need to integrate the density over the region.
$endgroup$
– saulspatz
Mar 27 at 18:41
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Just like $textVolume=iiint 1dV$, we have $textWeight=iiinttextdensity,dV$. In fact, the volume calculation is a special case of the weight calculation: If the density is $1$, then the volume is the weight.
answered Mar 27 at 18:42
ArthurArthur
121k7121207
$endgroup$
$begingroup$
So this can only be done through triple integration? I'm currently studying for an exam and I've only learned up to double integration so maybe this is not something I should be studying for right now?
$endgroup$
– krauser126
Mar 27 at 18:53
$begingroup$
@krauser126 Triple integrals isn't anything more than double integrals. You have an integral whose integrand is an integral. Nesting it one more level doesn't really change anything.
$endgroup$
– Arthur
Mar 27 at 19:13
$begingroup$
Ahhh interesting. Doesn't seem too much more complex than double integrals. I think I managed to solve it. I got an answer of M = 6.5
$endgroup$
– krauser126
Mar 27 at 19:25
$begingroup$
@krauser126 That looks like the right answer.
$endgroup$
– Arthur
Mar 27 at 19:32
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%2f3164931%2ffinding-the-mass-of-a-region-given-a-density-function%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
$begingroup$
Just like $textVolume=iiint 1dV$, we have $textWeight=iiinttextdensity,dV$. In fact, the volume calculation is a special case of the weight calculation: If the density is $1$, then the volume is the weight.
answered Mar 27 at 18:42
ArthurArthur
121k7121207
$endgroup$
$begingroup$
So this can only be done through triple integration? I'm currently studying for an exam and I've only learned up to double integration so maybe this is not something I should be studying for right now?
$endgroup$
– krauser126
Mar 27 at 18:53
$begingroup$
@krauser126 Triple integrals isn't anything more than double integrals. You have an integral whose integrand is an integral. Nesting it one more level doesn't really change anything.
$endgroup$
– Arthur
Mar 27 at 19:13
$begingroup$
Ahhh interesting. Doesn't seem too much more complex than double integrals. I think I managed to solve it. I got an answer of M = 6.5
$endgroup$
– krauser126
Mar 27 at 19:25
$begingroup$
@krauser126 That looks like the right answer.
$endgroup$
– Arthur
Mar 27 at 19:32
add a comment |
$begingroup$
Just like $textVolume=iiint 1dV$, we have $textWeight=iiinttextdensity,dV$. In fact, the volume calculation is a special case of the weight calculation: If the density is $1$, then the volume is the weight.
answered Mar 27 at 18:42
ArthurArthur
121k7121207
$endgroup$
$begingroup$
So this can only be done through triple integration? I'm currently studying for an exam and I've only learned up to double integration so maybe this is not something I should be studying for right now?
$endgroup$
– krauser126
Mar 27 at 18:53
$begingroup$
@krauser126 Triple integrals isn't anything more than double integrals. You have an integral whose integrand is an integral. Nesting it one more level doesn't really change anything.
$endgroup$
– Arthur
Mar 27 at 19:13
$begingroup$
Ahhh interesting. Doesn't seem too much more complex than double integrals. I think I managed to solve it. I got an answer of M = 6.5
$endgroup$
– krauser126
Mar 27 at 19:25
$begingroup$
@krauser126 That looks like the right answer.
$endgroup$
– Arthur
Mar 27 at 19:32
add a comment |
$begingroup$
Just like $textVolume=iiint 1dV$, we have $textWeight=iiinttextdensity,dV$. In fact, the volume calculation is a special case of the weight calculation: If the density is $1$, then the volume is the weight.
answered Mar 27 at 18:42
ArthurArthur
121k7121207
$endgroup$
Just like $textVolume=iiint 1dV$, we have $textWeight=iiinttextdensity,dV$. In fact, the volume calculation is a special case of the weight calculation: If the density is $1$, then the volume is the weight.
answered Mar 27 at 18:42
ArthurArthur
121k7121207
answered Mar 27 at 18:42
ArthurArthur
121k7121207
answered Mar 27 at 18:42
ArthurArthur
121k7121207
answered Mar 27 at 18:42
ArthurArthur
121k7121207
121k7121207
$begingroup$
So this can only be done through triple integration? I'm currently studying for an exam and I've only learned up to double integration so maybe this is not something I should be studying for right now?
$endgroup$
– krauser126
Mar 27 at 18:53
$begingroup$
@krauser126 Triple integrals isn't anything more than double integrals. You have an integral whose integrand is an integral. Nesting it one more level doesn't really change anything.
$endgroup$
– Arthur
Mar 27 at 19:13
$begingroup$
Ahhh interesting. Doesn't seem too much more complex than double integrals. I think I managed to solve it. I got an answer of M = 6.5
$endgroup$
– krauser126
Mar 27 at 19:25
$begingroup$
@krauser126 That looks like the right answer.
$endgroup$
– Arthur
Mar 27 at 19:32
add a comment |
$begingroup$
So this can only be done through triple integration? I'm currently studying for an exam and I've only learned up to double integration so maybe this is not something I should be studying for right now?
$endgroup$
– krauser126
Mar 27 at 18:53
$begingroup$
@krauser126 Triple integrals isn't anything more than double integrals. You have an integral whose integrand is an integral. Nesting it one more level doesn't really change anything.
$endgroup$
– Arthur
Mar 27 at 19:13
$begingroup$
Ahhh interesting. Doesn't seem too much more complex than double integrals. I think I managed to solve it. I got an answer of M = 6.5
$endgroup$
– krauser126
Mar 27 at 19:25
$begingroup$
@krauser126 That looks like the right answer.
$endgroup$
– Arthur
Mar 27 at 19:32
$begingroup$
So this can only be done through triple integration? I'm currently studying for an exam and I've only learned up to double integration so maybe this is not something I should be studying for right now?
$endgroup$
– krauser126
Mar 27 at 18:53
$begingroup$
So this can only be done through triple integration? I'm currently studying for an exam and I've only learned up to double integration so maybe this is not something I should be studying for right now?
$endgroup$
– krauser126
Mar 27 at 18:53
$begingroup$
@krauser126 Triple integrals isn't anything more than double integrals. You have an integral whose integrand is an integral. Nesting it one more level doesn't really change anything.
$endgroup$
– Arthur
Mar 27 at 19:13
$begingroup$
@krauser126 Triple integrals isn't anything more than double integrals. You have an integral whose integrand is an integral. Nesting it one more level doesn't really change anything.
$endgroup$
– Arthur
Mar 27 at 19:13
$begingroup$
Ahhh interesting. Doesn't seem too much more complex than double integrals. I think I managed to solve it. I got an answer of M = 6.5
$endgroup$
– krauser126
Mar 27 at 19:25
$begingroup$
Ahhh interesting. Doesn't seem too much more complex than double integrals. I think I managed to solve it. I got an answer of M = 6.5
$endgroup$
– krauser126
Mar 27 at 19:25
$begingroup$
@krauser126 That looks like the right answer.
$endgroup$
– Arthur
Mar 27 at 19:32
$begingroup$
@krauser126 That looks like the right answer.
$endgroup$
– Arthur
Mar 27 at 19:32
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%2f3164931%2ffinding-the-mass-of-a-region-given-a-density-function%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
$begingroup$
You just need to integrate the density over the region.
$endgroup$
– saulspatz
Mar 27 at 18:41