Computing Triple Integral Using Spherical Coordinates
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I just have trouble finding the bounds for phi in this problem. So far I found $pi < theta < 3pi/2$ and $0 < rho < sqrt{10}$
Use spherical coordinates to calculate the triple integral of $f(x,y,z) = y$ over the region $$x^2+y^2+z^2= 10$$ and $$x,y,z ≤ 0$$
calculus integration spherical-coordinates
edited 6 hours ago
MathFun123
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asked 6 hours ago
MathCoolGuy99
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up vote
0
down vote
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I just have trouble finding the bounds for phi in this problem. So far I found $pi < theta < 3pi/2$ and $0 < rho < sqrt{10}$
Use spherical coordinates to calculate the triple integral of $f(x,y,z) = y$ over the region $$x^2+y^2+z^2= 10$$ and $$x,y,z ≤ 0$$
calculus integration spherical-coordinates
edited 6 hours ago
MathFun123
439216
asked 6 hours ago
MathCoolGuy99
42
New contributor
MathCoolGuy99 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Welcome to MSE. It will be more likely that you will get an answer if you show us that you made an effort. This should be added to the question rather than in the comments.
– José Carlos Santos
6 hours ago
What is $p$? In spherical coordinates you have the modulus and two angles, is $p$ the modulus? I think you should explicitly write the integral both in Cartesian and in spherical coordinates and see if it looks okay. It would be easier for us to check your result as well
– Yuriy S
6 hours ago
Hi, p is rho. My apology for the notation confusion.
– MathCoolGuy99
6 hours ago
@MathCoolGuy99 $dfrac{pi}{2}leqphileqpi$.
– Nosrati
5 hours ago
@Tom, please read the problem statement. The integration is only over the part of a sphere in one octant
– Yuriy S
4 hours ago
|
show 2 more comments
up vote
0
down vote
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up vote
0
down vote
favorite
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1
I just have trouble finding the bounds for phi in this problem. So far I found $pi < theta < 3pi/2$ and $0 < rho < sqrt{10}$
Use spherical coordinates to calculate the triple integral of $f(x,y,z) = y$ over the region $$x^2+y^2+z^2= 10$$ and $$x,y,z ≤ 0$$
calculus integration spherical-coordinates
edited 6 hours ago
MathFun123
439216
asked 6 hours ago
MathCoolGuy99
42
New contributor
MathCoolGuy99 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
I just have trouble finding the bounds for phi in this problem. So far I found $pi < theta < 3pi/2$ and $0 < rho < sqrt{10}$
Use spherical coordinates to calculate the triple integral of $f(x,y,z) = y$ over the region $$x^2+y^2+z^2= 10$$ and $$x,y,z ≤ 0$$
calculus integration spherical-coordinates
calculus integration spherical-coordinates
edited 6 hours ago
MathFun123
439216
asked 6 hours ago
MathCoolGuy99
42
New contributor
MathCoolGuy99 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 6 hours ago
MathFun123
439216
asked 6 hours ago
MathCoolGuy99
42
New contributor
MathCoolGuy99 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 6 hours ago
MathFun123
439216
edited 6 hours ago
MathFun123
439216
edited 6 hours ago
MathFun123
439216
439216
asked 6 hours ago
MathCoolGuy99
42
New contributor
MathCoolGuy99 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 6 hours ago
MathCoolGuy99
42
asked 6 hours ago
MathCoolGuy99
42
42
New contributor
MathCoolGuy99 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
MathCoolGuy99 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
MathCoolGuy99 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Welcome to MSE. It will be more likely that you will get an answer if you show us that you made an effort. This should be added to the question rather than in the comments.
– José Carlos Santos
6 hours ago
What is $p$? In spherical coordinates you have the modulus and two angles, is $p$ the modulus? I think you should explicitly write the integral both in Cartesian and in spherical coordinates and see if it looks okay. It would be easier for us to check your result as well
– Yuriy S
6 hours ago
Hi, p is rho. My apology for the notation confusion.
– MathCoolGuy99
6 hours ago
@MathCoolGuy99 $dfrac{pi}{2}leqphileqpi$.
– Nosrati
5 hours ago
@Tom, please read the problem statement. The integration is only over the part of a sphere in one octant
– Yuriy S
4 hours ago
|
show 2 more comments
Welcome to MSE. It will be more likely that you will get an answer if you show us that you made an effort. This should be added to the question rather than in the comments.
– José Carlos Santos
6 hours ago
What is $p$? In spherical coordinates you have the modulus and two angles, is $p$ the modulus? I think you should explicitly write the integral both in Cartesian and in spherical coordinates and see if it looks okay. It would be easier for us to check your result as well
– Yuriy S
6 hours ago
Hi, p is rho. My apology for the notation confusion.
– MathCoolGuy99
6 hours ago
@MathCoolGuy99 $dfrac{pi}{2}leqphileqpi$.
– Nosrati
5 hours ago
@Tom, please read the problem statement. The integration is only over the part of a sphere in one octant
– Yuriy S
4 hours ago
Welcome to MSE. It will be more likely that you will get an answer if you show us that you made an effort. This should be added to the question rather than in the comments.
– José Carlos Santos
6 hours ago
Welcome to MSE. It will be more likely that you will get an answer if you show us that you made an effort. This should be added to the question rather than in the comments.
– José Carlos Santos
6 hours ago
What is $p$? In spherical coordinates you have the modulus and two angles, is $p$ the modulus? I think you should explicitly write the integral both in Cartesian and in spherical coordinates and see if it looks okay. It would be easier for us to check your result as well
– Yuriy S
6 hours ago
What is $p$? In spherical coordinates you have the modulus and two angles, is $p$ the modulus? I think you should explicitly write the integral both in Cartesian and in spherical coordinates and see if it looks okay. It would be easier for us to check your result as well
– Yuriy S
6 hours ago
Hi, p is rho. My apology for the notation confusion.
– MathCoolGuy99
6 hours ago
Hi, p is rho. My apology for the notation confusion.
– MathCoolGuy99
6 hours ago
@MathCoolGuy99 $dfrac{pi}{2}leqphileqpi$.
– Nosrati
5 hours ago
@MathCoolGuy99 $dfrac{pi}{2}leqphileqpi$.
– Nosrati
5 hours ago
@Tom, please read the problem statement. The integration is only over the part of a sphere in one octant
– Yuriy S
4 hours ago
@Tom, please read the problem statement. The integration is only over the part of a sphere in one octant
– Yuriy S
4 hours ago
|
show 2 more comments
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Welcome to MSE. It will be more likely that you will get an answer if you show us that you made an effort. This should be added to the question rather than in the comments.
– José Carlos Santos
6 hours ago
What is $p$? In spherical coordinates you have the modulus and two angles, is $p$ the modulus? I think you should explicitly write the integral both in Cartesian and in spherical coordinates and see if it looks okay. It would be easier for us to check your result as well
– Yuriy S
6 hours ago
Hi, p is rho. My apology for the notation confusion.
– MathCoolGuy99
6 hours ago
@MathCoolGuy99 $dfrac{pi}{2}leqphileqpi$.
– Nosrati
5 hours ago
@Tom, please read the problem statement. The integration is only over the part of a sphere in one octant
– Yuriy S
4 hours ago