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Difficulty understanding an integration identity
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in reading a textbook recently I've come across an identity that I can't derive, even though it looks like it should be easy:
$$ lim _x_0 to infty int d^3vecx~-~ lim _x_0 to -infty int d^3vecx ~equiv~ int d^4x fracpartialpartial x_0 ,
$$
where as usual $(x_0, vecx)$ is a point in space-time.
Any hints/help in deriving this is appreciated.
integration calculus
migrated from physics.stackexchange.com Jul 20 at 20:55
This question came from our site for active researchers, academics and students of physics.
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in reading a textbook recently I've come across an identity that I can't derive, even though it looks like it should be easy:
$$ lim _x_0 to infty int d^3vecx~-~ lim _x_0 to -infty int d^3vecx ~equiv~ int d^4x fracpartialpartial x_0 ,
$$
where as usual $(x_0, vecx)$ is a point in space-time.
Any hints/help in deriving this is appreciated.
integration calculus
migrated from physics.stackexchange.com Jul 20 at 20:55
This question came from our site for active researchers, academics and students of physics.
1
Use the fundamental theorem of calculus
– Slereah
Jul 19 at 6:20
Thanks for the help! Particularly the edit - I was mostly confused by the notation.
– Quizeloni
Jul 19 at 9:15
Are these supposed to be considered as operators? (i.e., essentially, should there be some function of $(x_0, vecx)$ under the integral signs here, with appropriate properties to make the integrals convergent?)
– Steven Stadnicki
Jul 20 at 21:01
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
in reading a textbook recently I've come across an identity that I can't derive, even though it looks like it should be easy:
$$ lim _x_0 to infty int d^3vecx~-~ lim _x_0 to -infty int d^3vecx ~equiv~ int d^4x fracpartialpartial x_0 ,
$$
where as usual $(x_0, vecx)$ is a point in space-time.
Any hints/help in deriving this is appreciated.
integration calculus
in reading a textbook recently I've come across an identity that I can't derive, even though it looks like it should be easy:
$$ lim _x_0 to infty int d^3vecx~-~ lim _x_0 to -infty int d^3vecx ~equiv~ int d^4x fracpartialpartial x_0 ,
$$
where as usual $(x_0, vecx)$ is a point in space-time.
Any hints/help in deriving this is appreciated.
integration calculus
asked Jul 19 at 5:38
Quizeloni
migrated from physics.stackexchange.com Jul 20 at 20:55
This question came from our site for active researchers, academics and students of physics.
migrated from physics.stackexchange.com Jul 20 at 20:55
This question came from our site for active researchers, academics and students of physics.
1
Use the fundamental theorem of calculus
– Slereah
Jul 19 at 6:20
Thanks for the help! Particularly the edit - I was mostly confused by the notation.
– Quizeloni
Jul 19 at 9:15
Are these supposed to be considered as operators? (i.e., essentially, should there be some function of $(x_0, vecx)$ under the integral signs here, with appropriate properties to make the integrals convergent?)
– Steven Stadnicki
Jul 20 at 21:01
add a comment |Â
1
Use the fundamental theorem of calculus
– Slereah
Jul 19 at 6:20
Thanks for the help! Particularly the edit - I was mostly confused by the notation.
– Quizeloni
Jul 19 at 9:15
Are these supposed to be considered as operators? (i.e., essentially, should there be some function of $(x_0, vecx)$ under the integral signs here, with appropriate properties to make the integrals convergent?)
– Steven Stadnicki
Jul 20 at 21:01
1
1
Use the fundamental theorem of calculus
– Slereah
Jul 19 at 6:20
Use the fundamental theorem of calculus
– Slereah
Jul 19 at 6:20
Thanks for the help! Particularly the edit - I was mostly confused by the notation.
– Quizeloni
Jul 19 at 9:15
Thanks for the help! Particularly the edit - I was mostly confused by the notation.
– Quizeloni
Jul 19 at 9:15
Are these supposed to be considered as operators? (i.e., essentially, should there be some function of $(x_0, vecx)$ under the integral signs here, with appropriate properties to make the integrals convergent?)
– Steven Stadnicki
Jul 20 at 21:01
Are these supposed to be considered as operators? (i.e., essentially, should there be some function of $(x_0, vecx)$ under the integral signs here, with appropriate properties to make the integrals convergent?)
– Steven Stadnicki
Jul 20 at 21:01
add a comment |Â
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1
Use the fundamental theorem of calculus
– Slereah
Jul 19 at 6:20
Thanks for the help! Particularly the edit - I was mostly confused by the notation.
– Quizeloni
Jul 19 at 9:15
Are these supposed to be considered as operators? (i.e., essentially, should there be some function of $(x_0, vecx)$ under the integral signs here, with appropriate properties to make the integrals convergent?)
– Steven Stadnicki
Jul 20 at 21:01