sketch the region of integration for $int_0^2 int_0^x int_0^y f(x,y,z) ,dz,dy,dx$ [closed]

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$$int_0^2 int_0^x int_0^y f(x,y,z) ,dz,dy,dx$$

From what I can understand that the region should be between planes $x=0$, $x=2$ and $y=0$, $y=x$ and $z=0$, $z=y$.

I am finding it very difficult to represent it on a piece of paper. Please advise.

integration multivariable-calculus

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edited Jul 20 at 23:56

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asked Jul 20 at 22:33

thepanda

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closed as off-topic by user21820, Xander Henderson, Isaac Browne, Nils Matthes, Taroccoesbrocco Jul 26 at 7:41

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – user21820, Xander Henderson, Isaac Browne, Nils Matthes, Taroccoesbrocco

If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  

  
  
  
  
  
  

  
  If you at least have an idea, I recommend drawing it out and checking that the integration boundaries make sense for your surface. Wrong or right, I've found this helps to gain some geometric intuition for the problem (and if wrong, hopefully suggests a correction)
  – Brevan Ellefsen
  Jul 20 at 22:42
  

  
  
  
  

add a comment | 

up vote
1
down vote

favorite

1

$$int_0^2 int_0^x int_0^y f(x,y,z) ,dz,dy,dx$$

From what I can understand that the region should be between planes $x=0$, $x=2$ and $y=0$, $y=x$ and $z=0$, $z=y$.

I am finding it very difficult to represent it on a piece of paper. Please advise.

integration multivariable-calculus

share|cite|improve this question

edited Jul 20 at 23:56

Community♦

1

asked Jul 20 at 22:33

thepanda

695

closed as off-topic by user21820, Xander Henderson, Isaac Browne, Nils Matthes, Taroccoesbrocco Jul 26 at 7:41

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – user21820, Xander Henderson, Isaac Browne, Nils Matthes, Taroccoesbrocco

If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  

  
  
  
  
  
  

  
  If you at least have an idea, I recommend drawing it out and checking that the integration boundaries make sense for your surface. Wrong or right, I've found this helps to gain some geometric intuition for the problem (and if wrong, hopefully suggests a correction)
  – Brevan Ellefsen
  Jul 20 at 22:42
  

  
  
  
  

add a comment | 

up vote
1
down vote

favorite

1

up vote
1
down vote

favorite

1

1

$$int_0^2 int_0^x int_0^y f(x,y,z) ,dz,dy,dx$$

From what I can understand that the region should be between planes $x=0$, $x=2$ and $y=0$, $y=x$ and $z=0$, $z=y$.

I am finding it very difficult to represent it on a piece of paper. Please advise.

integration multivariable-calculus

share|cite|improve this question

edited Jul 20 at 23:56

Community♦

1

asked Jul 20 at 22:33

thepanda

695

$$int_0^2 int_0^x int_0^y f(x,y,z) ,dz,dy,dx$$

From what I can understand that the region should be between planes $x=0$, $x=2$ and $y=0$, $y=x$ and $z=0$, $z=y$.

I am finding it very difficult to represent it on a piece of paper. Please advise.

integration multivariable-calculus

share|cite|improve this question

edited Jul 20 at 23:56

Community♦

1

asked Jul 20 at 22:33

thepanda

695

share|cite|improve this question

share|cite|improve this question

edited Jul 20 at 23:56

Community♦

1

edited Jul 20 at 23:56

Community♦

1

edited Jul 20 at 23:56

Community♦

1

1

asked Jul 20 at 22:33

thepanda

695

asked Jul 20 at 22:33

thepanda

695

asked Jul 20 at 22:33

thepanda

695

695

closed as off-topic by user21820, Xander Henderson, Isaac Browne, Nils Matthes, Taroccoesbrocco Jul 26 at 7:41

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – user21820, Xander Henderson, Isaac Browne, Nils Matthes, Taroccoesbrocco

If this question can be reworded to fit the rules in the help center, please edit the question.

closed as off-topic by user21820, Xander Henderson, Isaac Browne, Nils Matthes, Taroccoesbrocco Jul 26 at 7:41

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – user21820, Xander Henderson, Isaac Browne, Nils Matthes, Taroccoesbrocco

If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  

  
  
  
  
  
  

  
  If you at least have an idea, I recommend drawing it out and checking that the integration boundaries make sense for your surface. Wrong or right, I've found this helps to gain some geometric intuition for the problem (and if wrong, hopefully suggests a correction)
  – Brevan Ellefsen
  Jul 20 at 22:42
  

  
  
  
  

add a comment | 

• 
  
  
  

  
  

  
  
  
  
  
  

  
  If you at least have an idea, I recommend drawing it out and checking that the integration boundaries make sense for your surface. Wrong or right, I've found this helps to gain some geometric intuition for the problem (and if wrong, hopefully suggests a correction)
  – Brevan Ellefsen
  Jul 20 at 22:42
  

  
  
  
  

If you at least have an idea, I recommend drawing it out and checking that the integration boundaries make sense for your surface. Wrong or right, I've found this helps to gain some geometric intuition for the problem (and if wrong, hopefully suggests a correction)
– Brevan Ellefsen
Jul 20 at 22:42

If you at least have an idea, I recommend drawing it out and checking that the integration boundaries make sense for your surface. Wrong or right, I've found this helps to gain some geometric intuition for the problem (and if wrong, hopefully suggests a correction)
– Brevan Ellefsen
Jul 20 at 22:42

add a comment | 

3 Answers
3

active

oldest

votes

up vote
1
down vote



accepted

Yes you are right the limit to consider are

• $0le x le 2$ varing along $x$ axis


• $0le y le x$ varing in $x-y$ plane between $x$ axis and the line $y=x$


• $0le z le y$ varing in space between $x-y$ plane and the plane $z=y$

A good way to vizualize without a 3D plot program is try to make at first some sketch in the $x-y$, $y-z$, $x-z$ planes and then try to vizualize the region in 3D.

Here below an example

share|cite|improve this answer

edited Jul 20 at 23:15

answered Jul 20 at 22:49

gimusi

65.4k73584

add a comment | 

up vote
1
down vote

Here is the integration region:

share|cite|improve this answer

answered Jul 20 at 22:44

David G. Stork

7,6652929

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Thanks a lot! but I am solving a question from the book and I have to answer it on a paper. I don't know how to represent it on a paper.
  – thepanda
  Jul 20 at 22:48
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Sketch my figure with pen and paper. Mark the corner points and simply draw straight lines between them.
  – David G. Stork
  Jul 20 at 22:48
  
  

  
  
  
  

add a comment | 

up vote
1
down vote

Drawing cross-sections may be beneficial.

$x=0, x=2$ and $y=0, y=x$ define a right triangular prism, infinite in the $z$-direction. Draw its cross-section in the $z=c$ plane (I'd probably consider $c=0$ here for the $xy$-plane).

Now consider the intersections with $z=0$, if you haven't done so, and $z=y$. The former gives a right triangular base, and the latter cuts through your prism at a $pi/4$ angle.

You could consider drawing the cross-section from another perspective as well - say choosing three projections flattening one of the cartesian components.

share|cite|improve this answer

answered Jul 20 at 22:51

zahbaz

7,52721636

add a comment | 

3 Answers
3

active

oldest

votes

3 Answers
3

active

oldest

votes

active

oldest

votes

active

oldest

votes

up vote
1
down vote



accepted

Yes you are right the limit to consider are

• $0le x le 2$ varing along $x$ axis


• $0le y le x$ varing in $x-y$ plane between $x$ axis and the line $y=x$


• $0le z le y$ varing in space between $x-y$ plane and the plane $z=y$

A good way to vizualize without a 3D plot program is try to make at first some sketch in the $x-y$, $y-z$, $x-z$ planes and then try to vizualize the region in 3D.

Here below an example

share|cite|improve this answer

edited Jul 20 at 23:15

answered Jul 20 at 22:49

gimusi

65.4k73584

add a comment | 

up vote
1
down vote



accepted

Yes you are right the limit to consider are

• $0le x le 2$ varing along $x$ axis


• $0le y le x$ varing in $x-y$ plane between $x$ axis and the line $y=x$


• $0le z le y$ varing in space between $x-y$ plane and the plane $z=y$

A good way to vizualize without a 3D plot program is try to make at first some sketch in the $x-y$, $y-z$, $x-z$ planes and then try to vizualize the region in 3D.

Here below an example

share|cite|improve this answer

edited Jul 20 at 23:15

answered Jul 20 at 22:49

gimusi

65.4k73584

add a comment | 

up vote
1
down vote



accepted

up vote
1
down vote



accepted

Yes you are right the limit to consider are

• $0le x le 2$ varing along $x$ axis


• $0le y le x$ varing in $x-y$ plane between $x$ axis and the line $y=x$


• $0le z le y$ varing in space between $x-y$ plane and the plane $z=y$

A good way to vizualize without a 3D plot program is try to make at first some sketch in the $x-y$, $y-z$, $x-z$ planes and then try to vizualize the region in 3D.

Here below an example

share|cite|improve this answer

edited Jul 20 at 23:15

answered Jul 20 at 22:49

gimusi

65.4k73584

Yes you are right the limit to consider are

• $0le x le 2$ varing along $x$ axis


• $0le y le x$ varing in $x-y$ plane between $x$ axis and the line $y=x$


• $0le z le y$ varing in space between $x-y$ plane and the plane $z=y$

A good way to vizualize without a 3D plot program is try to make at first some sketch in the $x-y$, $y-z$, $x-z$ planes and then try to vizualize the region in 3D.

Here below an example

share|cite|improve this answer

edited Jul 20 at 23:15

answered Jul 20 at 22:49

gimusi

65.4k73584

share|cite|improve this answer

share|cite|improve this answer

edited Jul 20 at 23:15

edited Jul 20 at 23:15

edited Jul 20 at 23:15

answered Jul 20 at 22:49

gimusi

65.4k73584

answered Jul 20 at 22:49

gimusi

65.4k73584

answered Jul 20 at 22:49

gimusi

65.4k73584

65.4k73584

add a comment | 

add a comment | 

up vote
1
down vote

Here is the integration region:

share|cite|improve this answer

answered Jul 20 at 22:44

David G. Stork

7,6652929

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Thanks a lot! but I am solving a question from the book and I have to answer it on a paper. I don't know how to represent it on a paper.
  – thepanda
  Jul 20 at 22:48
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Sketch my figure with pen and paper. Mark the corner points and simply draw straight lines between them.
  – David G. Stork
  Jul 20 at 22:48
  
  

  
  
  
  

add a comment | 

up vote
1
down vote

Here is the integration region:

share|cite|improve this answer

answered Jul 20 at 22:44

David G. Stork

7,6652929

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Thanks a lot! but I am solving a question from the book and I have to answer it on a paper. I don't know how to represent it on a paper.
  – thepanda
  Jul 20 at 22:48
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Sketch my figure with pen and paper. Mark the corner points and simply draw straight lines between them.
  – David G. Stork
  Jul 20 at 22:48
  
  

  
  
  
  

add a comment | 

up vote
1
down vote

up vote
1
down vote

Here is the integration region:

share|cite|improve this answer

answered Jul 20 at 22:44

David G. Stork

7,6652929

Here is the integration region:

share|cite|improve this answer

answered Jul 20 at 22:44

David G. Stork

7,6652929

share|cite|improve this answer

share|cite|improve this answer

answered Jul 20 at 22:44

David G. Stork

7,6652929

answered Jul 20 at 22:44

David G. Stork

7,6652929

answered Jul 20 at 22:44

David G. Stork

7,6652929

7,6652929

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Thanks a lot! but I am solving a question from the book and I have to answer it on a paper. I don't know how to represent it on a paper.
  – thepanda
  Jul 20 at 22:48
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Sketch my figure with pen and paper. Mark the corner points and simply draw straight lines between them.
  – David G. Stork
  Jul 20 at 22:48
  
  

  
  
  
  

add a comment | 

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Thanks a lot! but I am solving a question from the book and I have to answer it on a paper. I don't know how to represent it on a paper.
  – thepanda
  Jul 20 at 22:48
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Sketch my figure with pen and paper. Mark the corner points and simply draw straight lines between them.
  – David G. Stork
  Jul 20 at 22:48
  
  

  
  
  
  

Thanks a lot! but I am solving a question from the book and I have to answer it on a paper. I don't know how to represent it on a paper.
– thepanda
Jul 20 at 22:48

Thanks a lot! but I am solving a question from the book and I have to answer it on a paper. I don't know how to represent it on a paper.
– thepanda
Jul 20 at 22:48

Sketch my figure with pen and paper. Mark the corner points and simply draw straight lines between them.
– David G. Stork
Jul 20 at 22:48

Sketch my figure with pen and paper. Mark the corner points and simply draw straight lines between them.
– David G. Stork
Jul 20 at 22:48

add a comment | 

up vote
1
down vote

Drawing cross-sections may be beneficial.

$x=0, x=2$ and $y=0, y=x$ define a right triangular prism, infinite in the $z$-direction. Draw its cross-section in the $z=c$ plane (I'd probably consider $c=0$ here for the $xy$-plane).

Now consider the intersections with $z=0$, if you haven't done so, and $z=y$. The former gives a right triangular base, and the latter cuts through your prism at a $pi/4$ angle.

You could consider drawing the cross-section from another perspective as well - say choosing three projections flattening one of the cartesian components.

share|cite|improve this answer

answered Jul 20 at 22:51

zahbaz

7,52721636

add a comment | 

up vote
1
down vote

Drawing cross-sections may be beneficial.

$x=0, x=2$ and $y=0, y=x$ define a right triangular prism, infinite in the $z$-direction. Draw its cross-section in the $z=c$ plane (I'd probably consider $c=0$ here for the $xy$-plane).

Now consider the intersections with $z=0$, if you haven't done so, and $z=y$. The former gives a right triangular base, and the latter cuts through your prism at a $pi/4$ angle.

You could consider drawing the cross-section from another perspective as well - say choosing three projections flattening one of the cartesian components.

share|cite|improve this answer

answered Jul 20 at 22:51

zahbaz

7,52721636

add a comment | 

up vote
1
down vote

up vote
1
down vote

Drawing cross-sections may be beneficial.

$x=0, x=2$ and $y=0, y=x$ define a right triangular prism, infinite in the $z$-direction. Draw its cross-section in the $z=c$ plane (I'd probably consider $c=0$ here for the $xy$-plane).

Now consider the intersections with $z=0$, if you haven't done so, and $z=y$. The former gives a right triangular base, and the latter cuts through your prism at a $pi/4$ angle.

You could consider drawing the cross-section from another perspective as well - say choosing three projections flattening one of the cartesian components.

share|cite|improve this answer

answered Jul 20 at 22:51

zahbaz

7,52721636

Drawing cross-sections may be beneficial.

$x=0, x=2$ and $y=0, y=x$ define a right triangular prism, infinite in the $z$-direction. Draw its cross-section in the $z=c$ plane (I'd probably consider $c=0$ here for the $xy$-plane).

Now consider the intersections with $z=0$, if you haven't done so, and $z=y$. The former gives a right triangular base, and the latter cuts through your prism at a $pi/4$ angle.

You could consider drawing the cross-section from another perspective as well - say choosing three projections flattening one of the cartesian components.

share|cite|improve this answer

answered Jul 20 at 22:51

zahbaz

7,52721636

share|cite|improve this answer

share|cite|improve this answer

answered Jul 20 at 22:51

zahbaz

7,52721636

answered Jul 20 at 22:51

zahbaz

7,52721636

answered Jul 20 at 22:51

zahbaz

7,52721636

7,52721636

add a comment | 

add a comment |