Fdtxjr

Effects on objects due to a brief relocation of massive amounts of mass

Belief In God or Knowledge Of God. Which is better?

Did Mueller's report provide an evidentiary basis for the claim of Russian govt election interference via social media?

Is CEO the "profession" with the most psychopaths?

How to unroll a parameter pack from right to left

What is "gratricide"?

How come Sam didn't become Lord of Horn Hill?

What does it mean that physics no longer uses mechanical models to describe phenomena?

How would a mousetrap for use in space work?

How does the secondary effect of the Heat Metal spell interact with a creature resistant/immune to fire damage?

What initially awakened the Balrog?

Triggering an ultrasonic sensor

Hangman Game with C++

How to make a Field only accept Numbers in Magento 2

If Windows 7 doesn't support WSL, then what does Linux subsystem option mean?

How many time did Arya actually used needle?

AppleTVs create a chatty alternate WiFi network

What would you call this weird metallic apparatus that allows you to lift people?

What do you call the main part of a joke?

Maximum summed subsequences with non-adjacent items

Why limits give us the exact value of the slope of the tangent line?

Co-worker has annoying ringtone

Should I use a zero-interest credit card for a large one-time purchase?

Find 108 by using 3,4,6

Find the volume of the tetrahedron using triple integrals

2

1

$begingroup$

Find the volume of the tetrahedron with vertices $(0,0,0), (0,0,1), (1,0,1), (0,1,1)$, equation $$x+y=z$$
bounded by $x=0$, $y=0$ and $z=1$.

Then $x+y=1$. My integral: is this correct?
$$int_0^1 int_0^z int_0^z-y ,dx,dy,dz$$

multivariable-calculus volume multiple-integral

share|cite|improve this question

edited Apr 9 '16 at 15:36

Τίμων

1,3382924

asked Apr 9 '16 at 13:13

MayaMaya

1719

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Welcome to Math Stack exchange. It is best to type out your steps rather than sending a picture. To do this you can use mathjax as shown in meta.math.stackexchange.com/questions/5020/….
  $endgroup$
  – Arbuja
  Apr 9 '16 at 13:30
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @Maya are you an engineering student?
  $endgroup$
  – Vinay5forPrime
  Apr 14 '16 at 15:50
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @Vinay5forPrime Yes
  $endgroup$
  – Maya
  Apr 14 '16 at 15:58
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Yes your limits are correct. But I did not understand the line $x+y=1$. There is not need for that. Please give steps to your solution. Check my work problems have a high potential to be put on hold.
  $endgroup$
  – Vinay5forPrime
  Apr 15 '16 at 18:40
  

  
  
  
  

add a comment | 

2

1

$begingroup$

Find the volume of the tetrahedron with vertices $(0,0,0), (0,0,1), (1,0,1), (0,1,1)$, equation $$x+y=z$$
bounded by $x=0$, $y=0$ and $z=1$.

Then $x+y=1$. My integral: is this correct?
$$int_0^1 int_0^z int_0^z-y ,dx,dy,dz$$

multivariable-calculus volume multiple-integral

share|cite|improve this question

edited Apr 9 '16 at 15:36

Τίμων

1,3382924

asked Apr 9 '16 at 13:13

MayaMaya

1719

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Welcome to Math Stack exchange. It is best to type out your steps rather than sending a picture. To do this you can use mathjax as shown in meta.math.stackexchange.com/questions/5020/….
  $endgroup$
  – Arbuja
  Apr 9 '16 at 13:30
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @Maya are you an engineering student?
  $endgroup$
  – Vinay5forPrime
  Apr 14 '16 at 15:50
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @Vinay5forPrime Yes
  $endgroup$
  – Maya
  Apr 14 '16 at 15:58
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Yes your limits are correct. But I did not understand the line $x+y=1$. There is not need for that. Please give steps to your solution. Check my work problems have a high potential to be put on hold.
  $endgroup$
  – Vinay5forPrime
  Apr 15 '16 at 18:40
  

  
  
  
  

add a comment | 

$begingroup$

Find the volume of the tetrahedron with vertices $(0,0,0), (0,0,1), (1,0,1), (0,1,1)$, equation $$x+y=z$$
bounded by $x=0$, $y=0$ and $z=1$.

Then $x+y=1$. My integral: is this correct?
$$int_0^1 int_0^z int_0^z-y ,dx,dy,dz$$

multivariable-calculus volume multiple-integral

share|cite|improve this question

edited Apr 9 '16 at 15:36

Τίμων

1,3382924

asked Apr 9 '16 at 13:13

MayaMaya

1719

$endgroup$

share|cite|improve this question

edited Apr 9 '16 at 15:36

Τίμων

1,3382924

asked Apr 9 '16 at 13:13

MayaMaya

1719

share|cite|improve this question

edited Apr 9 '16 at 15:36

Τίμων

1,3382924

asked Apr 9 '16 at 13:13

MayaMaya

1719

edited Apr 9 '16 at 15:36

Τίμων

1,3382924

edited Apr 9 '16 at 15:36

Τίμων

1,3382924

asked Apr 9 '16 at 13:13

MayaMaya

1719

asked Apr 9 '16 at 13:13

MayaMaya

1719

1 Answer
1

active

oldest

votes

0

$begingroup$

Your limit are correct, considering the YZ axis, if you want another example to understand better I have given the limits considering the XZ plane.

The tetrahedron is having it's base on the XZ plane and YZ plane so it will be a good idea to consider the limits from the XZ plane to the $x+y=z$ plane.

considering the limits from the YZ plane to the $x+y=z$

$y=0$ to $y=z-x$

Now as the limits for the volume has been take care of the area formed on the XZ plane is considered.
If the strip is considered paralled to the z axis then the limits

$z=x$ to $z=1$ and the limits of the x are $x=0$ to $x=1$ . This limit has been chosen to make it easier to solve the last integral using the Beta function.

The equation will be
$$int_0^1int_x^1int_0^z-xdy dz dx$$

share|cite|improve this answer

answered Apr 15 '16 at 18:41

Vinay5forPrimeVinay5forPrime

264414

$endgroup$

add a comment | 

Your Answer

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
);



);

draft saved

draft discarded

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

Name

Email

Required, but never shown

StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f1734604%2ffind-the-volume-of-the-tetrahedron-using-triple-integrals%23new-answer', 'question_page');

);

Post as a guest

Name

Email

Required, but never shown

0

$begingroup$

Your limit are correct, considering the YZ axis, if you want another example to understand better I have given the limits considering the XZ plane.

The tetrahedron is having it's base on the XZ plane and YZ plane so it will be a good idea to consider the limits from the XZ plane to the $x+y=z$ plane.

considering the limits from the YZ plane to the $x+y=z$

$y=0$ to $y=z-x$

Now as the limits for the volume has been take care of the area formed on the XZ plane is considered.
If the strip is considered paralled to the z axis then the limits

$z=x$ to $z=1$ and the limits of the x are $x=0$ to $x=1$ . This limit has been chosen to make it easier to solve the last integral using the Beta function.

The equation will be
$$int_0^1int_x^1int_0^z-xdy dz dx$$

share|cite|improve this answer

answered Apr 15 '16 at 18:41

Vinay5forPrimeVinay5forPrime

264414

$endgroup$

add a comment | 

0

$begingroup$

Your limit are correct, considering the YZ axis, if you want another example to understand better I have given the limits considering the XZ plane.

The tetrahedron is having it's base on the XZ plane and YZ plane so it will be a good idea to consider the limits from the XZ plane to the $x+y=z$ plane.

considering the limits from the YZ plane to the $x+y=z$

$y=0$ to $y=z-x$

Now as the limits for the volume has been take care of the area formed on the XZ plane is considered.
If the strip is considered paralled to the z axis then the limits

$z=x$ to $z=1$ and the limits of the x are $x=0$ to $x=1$ . This limit has been chosen to make it easier to solve the last integral using the Beta function.

The equation will be
$$int_0^1int_x^1int_0^z-xdy dz dx$$

share|cite|improve this answer

answered Apr 15 '16 at 18:41

Vinay5forPrimeVinay5forPrime

264414

$endgroup$

add a comment | 

$begingroup$

Your limit are correct, considering the YZ axis, if you want another example to understand better I have given the limits considering the XZ plane.

The tetrahedron is having it's base on the XZ plane and YZ plane so it will be a good idea to consider the limits from the XZ plane to the $x+y=z$ plane.

considering the limits from the YZ plane to the $x+y=z$

$y=0$ to $y=z-x$

Now as the limits for the volume has been take care of the area formed on the XZ plane is considered.
If the strip is considered paralled to the z axis then the limits

$z=x$ to $z=1$ and the limits of the x are $x=0$ to $x=1$ . This limit has been chosen to make it easier to solve the last integral using the Beta function.

The equation will be
$$int_0^1int_x^1int_0^z-xdy dz dx$$

share|cite|improve this answer

answered Apr 15 '16 at 18:41

Vinay5forPrimeVinay5forPrime

264414

$endgroup$

share|cite|improve this answer

answered Apr 15 '16 at 18:41

Vinay5forPrimeVinay5forPrime

264414

answered Apr 15 '16 at 18:41

Vinay5forPrimeVinay5forPrime

264414

answered Apr 15 '16 at 18:41

Vinay5forPrimeVinay5forPrime

264414