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 $$x,y,z ≤ 0$$










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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















up vote
0
down vote

favorite
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 $$x,y,z ≤ 0$$










share|cite|improve this question









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













up vote
0
down vote

favorite
1









up vote
0
down vote

favorite
1






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 $$x,y,z ≤ 0$$










share|cite|improve this question









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






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share|cite|improve this question









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edited 6 hours ago









MathFun123

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asked 6 hours ago









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MathCoolGuy99 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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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


















  • 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















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