Mixing
Evaluating the triple integral $iiint (x-2) ,dx,dy,dz$ over a region
$begingroup$
Here's the question
$$iiint (x-2) ,dx,dy,dz.$$
I am asked to evaluate this integral over the region $$D:=left { (x,y,z) inmathbb{R}^3 :1leq x^2+y^2+z^2 leq9,xleq z,z geq 0right }.$$
I tried to use the spherical coordinates find the solution :
$begin{cases} z=rho cosphi \ x=sinphi costheta \ z=sinphi sin theta end{cases}$
I obtained that:
- $ 0 leq rho leq 1 $
- $ 0 leq phi leq frac{pi}{2}$
- $ sin phi * cos thetaleq cos phi $
How can i obtain the value of $theta$ or $phi$ from the third inequality?
What can I do or what have I done wrong up until now?
Any support for this question would be appreciated.
integration multivariable-calculus definite-integrals
edited Jan 23 at 18:11
David G. Stork
11.1k41432
asked Jan 23 at 17:55
andrewandrew
698
$endgroup$
add a comment |
$begingroup$
Here's the question
$$iiint (x-2) ,dx,dy,dz.$$
I am asked to evaluate this integral over the region $$D:=left { (x,y,z) inmathbb{R}^3 :1leq x^2+y^2+z^2 leq9,xleq z,z geq 0right }.$$
I tried to use the spherical coordinates find the solution :
$begin{cases} z=rho cosphi \ x=sinphi costheta \ z=sinphi sin theta end{cases}$
I obtained that:
- $ 0 leq rho leq 1 $
- $ 0 leq phi leq frac{pi}{2}$
- $ sin phi * cos thetaleq cos phi $
How can i obtain the value of $theta$ or $phi$ from the third inequality?
What can I do or what have I done wrong up until now?
Any support for this question would be appreciated.
integration multivariable-calculus definite-integrals
edited Jan 23 at 18:11
David G. Stork
11.1k41432
asked Jan 23 at 17:55
andrewandrew
698
$endgroup$
add a comment |
$begingroup$
Here's the question
$$iiint (x-2) ,dx,dy,dz.$$
I am asked to evaluate this integral over the region $$D:=left { (x,y,z) inmathbb{R}^3 :1leq x^2+y^2+z^2 leq9,xleq z,z geq 0right }.$$
I tried to use the spherical coordinates find the solution :
$begin{cases} z=rho cosphi \ x=sinphi costheta \ z=sinphi sin theta end{cases}$
I obtained that:
- $ 0 leq rho leq 1 $
- $ 0 leq phi leq frac{pi}{2}$
- $ sin phi * cos thetaleq cos phi $
How can i obtain the value of $theta$ or $phi$ from the third inequality?
What can I do or what have I done wrong up until now?
Any support for this question would be appreciated.
integration multivariable-calculus definite-integrals
edited Jan 23 at 18:11
David G. Stork
11.1k41432
asked Jan 23 at 17:55
andrewandrew
698
$endgroup$
Here's the question
$$iiint (x-2) ,dx,dy,dz.$$
I am asked to evaluate this integral over the region $$D:=left { (x,y,z) inmathbb{R}^3 :1leq x^2+y^2+z^2 leq9,xleq z,z geq 0right }.$$
I tried to use the spherical coordinates find the solution :
$begin{cases} z=rho cosphi \ x=sinphi costheta \ z=sinphi sin theta end{cases}$
I obtained that:
- $ 0 leq rho leq 1 $
- $ 0 leq phi leq frac{pi}{2}$
- $ sin phi * cos thetaleq cos phi $
How can i obtain the value of $theta$ or $phi$ from the third inequality?
What can I do or what have I done wrong up until now?
Any support for this question would be appreciated.
integration multivariable-calculus definite-integrals
integration multivariable-calculus definite-integrals
edited Jan 23 at 18:11
David G. Stork
11.1k41432
asked Jan 23 at 17:55
andrewandrew
698
edited Jan 23 at 18:11
David G. Stork
11.1k41432
asked Jan 23 at 17:55
andrewandrew
698
edited Jan 23 at 18:11
David G. Stork
11.1k41432
edited Jan 23 at 18:11
David G. Stork
11.1k41432
edited Jan 23 at 18:11
David G. Stork
11.1k41432
11.1k41432
asked Jan 23 at 17:55
andrewandrew
698
asked Jan 23 at 17:55
andrewandrew
698
asked Jan 23 at 17:55
andrewandrew
698
698
add a comment |
add a comment |
1 Answer
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$begingroup$
Not an answer but "support for this question" (so please don't downvote): a figure to help visualization.
It is clear that the OP's inequality on radius is incorrect. Instead: $1 leq rho leq 3$
answered Jan 23 at 18:24
David G. StorkDavid G. Stork
11.1k41432
$endgroup$
add a comment |
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1 Answer
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1 Answer
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votes
$begingroup$
Not an answer but "support for this question" (so please don't downvote): a figure to help visualization.
It is clear that the OP's inequality on radius is incorrect. Instead: $1 leq rho leq 3$
answered Jan 23 at 18:24
David G. StorkDavid G. Stork
11.1k41432
$endgroup$
add a comment |
$begingroup$
Not an answer but "support for this question" (so please don't downvote): a figure to help visualization.
It is clear that the OP's inequality on radius is incorrect. Instead: $1 leq rho leq 3$
answered Jan 23 at 18:24
David G. StorkDavid G. Stork
11.1k41432
$endgroup$
add a comment |
$begingroup$
Not an answer but "support for this question" (so please don't downvote): a figure to help visualization.
It is clear that the OP's inequality on radius is incorrect. Instead: $1 leq rho leq 3$
answered Jan 23 at 18:24
David G. StorkDavid G. Stork
11.1k41432
$endgroup$
Not an answer but "support for this question" (so please don't downvote): a figure to help visualization.
It is clear that the OP's inequality on radius is incorrect. Instead: $1 leq rho leq 3$
answered Jan 23 at 18:24
David G. StorkDavid G. Stork
11.1k41432
edited Jan 23 at 18:32
answered Jan 23 at 18:24
David G. StorkDavid G. Stork
11.1k41432
answered Jan 23 at 18:24
David G. StorkDavid G. Stork
11.1k41432
answered Jan 23 at 18:24
David G. StorkDavid G. Stork
11.1k41432
11.1k41432
add a comment |
add a comment |
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