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Integrating in a spherical region using n-dimensional spherical coordinates
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I want to evaluate an integral of the form $int_{D}f(x_1,x_2,...x_n)dx_1dx_2...dx_n$ where $D$ is the $n$-dimensional spherical region lying between spheres of radii $r$ and $R$, $r<R$.
I want to use $n$-dimensional spherical coordinates (https://en.wikipedia.org/wiki/N-sphere#Spherical_coordinates).
I want to make sure if I am correct about setting the limits. Do I have to put outer limit as $r$ to $R$? And all other limits (that is, $0levarphi_ilepi$ for $i=1,2...n-2$ and $0levarphi_{n-1}<2pi$) will be unchanged as described in the Wikipedia article?
real-analysis calculus integration multivariable-calculus multiple-integral
asked Jan 14 at 1:03
ershersh
389113
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add a comment |
$begingroup$
I want to evaluate an integral of the form $int_{D}f(x_1,x_2,...x_n)dx_1dx_2...dx_n$ where $D$ is the $n$-dimensional spherical region lying between spheres of radii $r$ and $R$, $r<R$.
I want to use $n$-dimensional spherical coordinates (https://en.wikipedia.org/wiki/N-sphere#Spherical_coordinates).
I want to make sure if I am correct about setting the limits. Do I have to put outer limit as $r$ to $R$? And all other limits (that is, $0levarphi_ilepi$ for $i=1,2...n-2$ and $0levarphi_{n-1}<2pi$) will be unchanged as described in the Wikipedia article?
real-analysis calculus integration multivariable-calculus multiple-integral
asked Jan 14 at 1:03
ershersh
389113
$endgroup$
add a comment |
$begingroup$
I want to evaluate an integral of the form $int_{D}f(x_1,x_2,...x_n)dx_1dx_2...dx_n$ where $D$ is the $n$-dimensional spherical region lying between spheres of radii $r$ and $R$, $r<R$.
I want to use $n$-dimensional spherical coordinates (https://en.wikipedia.org/wiki/N-sphere#Spherical_coordinates).
I want to make sure if I am correct about setting the limits. Do I have to put outer limit as $r$ to $R$? And all other limits (that is, $0levarphi_ilepi$ for $i=1,2...n-2$ and $0levarphi_{n-1}<2pi$) will be unchanged as described in the Wikipedia article?
real-analysis calculus integration multivariable-calculus multiple-integral
asked Jan 14 at 1:03
ershersh
389113
$endgroup$
I want to evaluate an integral of the form $int_{D}f(x_1,x_2,...x_n)dx_1dx_2...dx_n$ where $D$ is the $n$-dimensional spherical region lying between spheres of radii $r$ and $R$, $r<R$.
I want to use $n$-dimensional spherical coordinates (https://en.wikipedia.org/wiki/N-sphere#Spherical_coordinates).
I want to make sure if I am correct about setting the limits. Do I have to put outer limit as $r$ to $R$? And all other limits (that is, $0levarphi_ilepi$ for $i=1,2...n-2$ and $0levarphi_{n-1}<2pi$) will be unchanged as described in the Wikipedia article?
real-analysis calculus integration multivariable-calculus multiple-integral
real-analysis calculus integration multivariable-calculus multiple-integral
asked Jan 14 at 1:03
ershersh
389113
asked Jan 14 at 1:03
ershersh
389113
asked Jan 14 at 1:03
ershersh
389113
asked Jan 14 at 1:03
ershersh
389113
asked Jan 14 at 1:03
ershersh
389113
389113
add a comment |
add a comment |
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