evaluating integral over surface of the sphere
Clash Royale CLAN TAG#URR8PPP
up vote
3
down vote
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This is what I've tried. Am I approaching this the right way? Also, where do I go next?
calculus integration multivariable-calculus
add a comment |Â
up vote
3
down vote
favorite
This is what I've tried. Am I approaching this the right way? Also, where do I go next?
calculus integration multivariable-calculus
1
Looks good so far. The inner antiderivative suggests $u=cos theta$ and that's good since then $du=-sin theta$ and you have the $sin theta$ where it's needed.
â coffeemath
Feb 15 '14 at 0:40
Há um erro: exp(a*cos(x)) != exp(a)*exp(cos(x))
â Rômulo Silva
Aug 27 at 17:06
add a comment |Â
up vote
3
down vote
favorite
up vote
3
down vote
favorite
This is what I've tried. Am I approaching this the right way? Also, where do I go next?
calculus integration multivariable-calculus
This is what I've tried. Am I approaching this the right way? Also, where do I go next?
calculus integration multivariable-calculus
asked Feb 14 '14 at 22:48
user120227
510517
510517
1
Looks good so far. The inner antiderivative suggests $u=cos theta$ and that's good since then $du=-sin theta$ and you have the $sin theta$ where it's needed.
â coffeemath
Feb 15 '14 at 0:40
Há um erro: exp(a*cos(x)) != exp(a)*exp(cos(x))
â Rômulo Silva
Aug 27 at 17:06
add a comment |Â
1
Looks good so far. The inner antiderivative suggests $u=cos theta$ and that's good since then $du=-sin theta$ and you have the $sin theta$ where it's needed.
â coffeemath
Feb 15 '14 at 0:40
Há um erro: exp(a*cos(x)) != exp(a)*exp(cos(x))
â Rômulo Silva
Aug 27 at 17:06
1
1
Looks good so far. The inner antiderivative suggests $u=cos theta$ and that's good since then $du=-sin theta$ and you have the $sin theta$ where it's needed.
â coffeemath
Feb 15 '14 at 0:40
Looks good so far. The inner antiderivative suggests $u=cos theta$ and that's good since then $du=-sin theta$ and you have the $sin theta$ where it's needed.
â coffeemath
Feb 15 '14 at 0:40
Há um erro: exp(a*cos(x)) != exp(a)*exp(cos(x))
â Rômulo Silva
Aug 27 at 17:06
Há um erro: exp(a*cos(x)) != exp(a)*exp(cos(x))
â Rômulo Silva
Aug 27 at 17:06
add a comment |Â
1 Answer
1
active
oldest
votes
up vote
1
down vote
accepted
the next steps are the following:
$$beginmatrix
iint_Se^z,dS&=&int_0^2piint_0^pie^a,costhetaa^2sintheta,dtheta dphi\
&=&a^2e^aint_0^2piint_0^pi e^costhetasintheta,dtheta dphi \
&=&2pi a^2e^aint_0^pi d(-e^costheta)\
&=&2pi a^2e^aleft(e-frac1eright)
endmatrix$$
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
accepted
the next steps are the following:
$$beginmatrix
iint_Se^z,dS&=&int_0^2piint_0^pie^a,costhetaa^2sintheta,dtheta dphi\
&=&a^2e^aint_0^2piint_0^pi e^costhetasintheta,dtheta dphi \
&=&2pi a^2e^aint_0^pi d(-e^costheta)\
&=&2pi a^2e^aleft(e-frac1eright)
endmatrix$$
add a comment |Â
up vote
1
down vote
accepted
the next steps are the following:
$$beginmatrix
iint_Se^z,dS&=&int_0^2piint_0^pie^a,costhetaa^2sintheta,dtheta dphi\
&=&a^2e^aint_0^2piint_0^pi e^costhetasintheta,dtheta dphi \
&=&2pi a^2e^aint_0^pi d(-e^costheta)\
&=&2pi a^2e^aleft(e-frac1eright)
endmatrix$$
add a comment |Â
up vote
1
down vote
accepted
up vote
1
down vote
accepted
the next steps are the following:
$$beginmatrix
iint_Se^z,dS&=&int_0^2piint_0^pie^a,costhetaa^2sintheta,dtheta dphi\
&=&a^2e^aint_0^2piint_0^pi e^costhetasintheta,dtheta dphi \
&=&2pi a^2e^aint_0^pi d(-e^costheta)\
&=&2pi a^2e^aleft(e-frac1eright)
endmatrix$$
the next steps are the following:
$$beginmatrix
iint_Se^z,dS&=&int_0^2piint_0^pie^a,costhetaa^2sintheta,dtheta dphi\
&=&a^2e^aint_0^2piint_0^pi e^costhetasintheta,dtheta dphi \
&=&2pi a^2e^aint_0^pi d(-e^costheta)\
&=&2pi a^2e^aleft(e-frac1eright)
endmatrix$$
answered Feb 15 '14 at 18:51
DiegoMath
1,9331021
1,9331021
add a comment |Â
add a comment |Â
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1
Looks good so far. The inner antiderivative suggests $u=cos theta$ and that's good since then $du=-sin theta$ and you have the $sin theta$ where it's needed.
â coffeemath
Feb 15 '14 at 0:40
Há um erro: exp(a*cos(x)) != exp(a)*exp(cos(x))
â Rômulo Silva
Aug 27 at 17:06