Is there a numerical method to solve a triple integral without numeric limits in its inner integrals
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Let's say I have this triple integral with this kind of limits:
$$
int _0^2:int_x^{8x}:int _0^y4xyz:dz:dy:dx:
$$
I wondering what numerical method I can use to solve it and eventually write a program/script to solve it. No symbolic solutions, no python+sympy.
Thanks.
Note: No need to solve it, just the right numeric method to solve this kind of integrals.
integration definite-integrals numerical-methods
asked Nov 24 at 0:28
Cliff
115
|
show 3 more comments
up vote
0
down vote
favorite
Let's say I have this triple integral with this kind of limits:
$$
int _0^2:int_x^{8x}:int _0^y4xyz:dz:dy:dx:
$$
I wondering what numerical method I can use to solve it and eventually write a program/script to solve it. No symbolic solutions, no python+sympy.
Thanks.
Note: No need to solve it, just the right numeric method to solve this kind of integrals.
integration definite-integrals numerical-methods
asked Nov 24 at 0:28
Cliff
115
python + scipy?
– Mark McClure
Nov 24 at 0:33
That's the second part! I need to be able to do it myself with a numeric method, then the computer.
– Cliff
Nov 24 at 0:34
The question is not clearly delimited / defined for my taste. What does it mean "numerically solve" or the "right numeric method" for (a) an integral with one variable and with fixed limits, (b) for the above integral (on a compact domain in $Bbb R^3$)? Why is the usual approach to solve integral after integral after integral, each integral numerically computed "with usual algorithms", not applicable?
– dan_fulea
Nov 24 at 0:41
Well then the answer might be just easier. What algorithm can I use without using a symbolic library? I can't just code a regular algorithm with those limits.
– Cliff
Nov 24 at 0:45
Simple algorithm (though not the best) to implement here is Monte Carlo integration. Make $n$ samples ${x,y,z}_i$ where you draw uniformly $xin[0,2]$ and $y,zin[0,16]$. Sum up $4xyz$ for the samples that satisfy $z<y$ and $x<y<8x$. Your integral is then this sum times $(16cdot 16cdot 2)/n$. The answer to $1%$ with $10^6$ samples.
– Winther
Nov 24 at 0:49
|
show 3 more comments
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Let's say I have this triple integral with this kind of limits:
$$
int _0^2:int_x^{8x}:int _0^y4xyz:dz:dy:dx:
$$
I wondering what numerical method I can use to solve it and eventually write a program/script to solve it. No symbolic solutions, no python+sympy.
Thanks.
Note: No need to solve it, just the right numeric method to solve this kind of integrals.
integration definite-integrals numerical-methods
asked Nov 24 at 0:28
Cliff
115
Let's say I have this triple integral with this kind of limits:
$$
int _0^2:int_x^{8x}:int _0^y4xyz:dz:dy:dx:
$$
I wondering what numerical method I can use to solve it and eventually write a program/script to solve it. No symbolic solutions, no python+sympy.
Thanks.
Note: No need to solve it, just the right numeric method to solve this kind of integrals.
integration definite-integrals numerical-methods
integration definite-integrals numerical-methods
asked Nov 24 at 0:28
Cliff
115
asked Nov 24 at 0:28
Cliff
115
edited Nov 24 at 0:35
asked Nov 24 at 0:28
Cliff
115
asked Nov 24 at 0:28
Cliff
115
asked Nov 24 at 0:28
Cliff
115
115
python + scipy?
– Mark McClure
Nov 24 at 0:33
That's the second part! I need to be able to do it myself with a numeric method, then the computer.
– Cliff
Nov 24 at 0:34
The question is not clearly delimited / defined for my taste. What does it mean "numerically solve" or the "right numeric method" for (a) an integral with one variable and with fixed limits, (b) for the above integral (on a compact domain in $Bbb R^3$)? Why is the usual approach to solve integral after integral after integral, each integral numerically computed "with usual algorithms", not applicable?
– dan_fulea
Nov 24 at 0:41
Well then the answer might be just easier. What algorithm can I use without using a symbolic library? I can't just code a regular algorithm with those limits.
– Cliff
Nov 24 at 0:45
Simple algorithm (though not the best) to implement here is Monte Carlo integration. Make $n$ samples ${x,y,z}_i$ where you draw uniformly $xin[0,2]$ and $y,zin[0,16]$. Sum up $4xyz$ for the samples that satisfy $z<y$ and $x<y<8x$. Your integral is then this sum times $(16cdot 16cdot 2)/n$. The answer to $1%$ with $10^6$ samples.
– Winther
Nov 24 at 0:49
|
show 3 more comments
python + scipy?
– Mark McClure
Nov 24 at 0:33
That's the second part! I need to be able to do it myself with a numeric method, then the computer.
– Cliff
Nov 24 at 0:34
The question is not clearly delimited / defined for my taste. What does it mean "numerically solve" or the "right numeric method" for (a) an integral with one variable and with fixed limits, (b) for the above integral (on a compact domain in $Bbb R^3$)? Why is the usual approach to solve integral after integral after integral, each integral numerically computed "with usual algorithms", not applicable?
– dan_fulea
Nov 24 at 0:41
Well then the answer might be just easier. What algorithm can I use without using a symbolic library? I can't just code a regular algorithm with those limits.
– Cliff
Nov 24 at 0:45
Simple algorithm (though not the best) to implement here is Monte Carlo integration. Make $n$ samples ${x,y,z}_i$ where you draw uniformly $xin[0,2]$ and $y,zin[0,16]$. Sum up $4xyz$ for the samples that satisfy $z<y$ and $x<y<8x$. Your integral is then this sum times $(16cdot 16cdot 2)/n$. The answer to $1%$ with $10^6$ samples.
– Winther
Nov 24 at 0:49
python + scipy?
– Mark McClure
Nov 24 at 0:33
python + scipy?
– Mark McClure
Nov 24 at 0:33
That's the second part! I need to be able to do it myself with a numeric method, then the computer.
– Cliff
Nov 24 at 0:34
That's the second part! I need to be able to do it myself with a numeric method, then the computer.
– Cliff
Nov 24 at 0:34
The question is not clearly delimited / defined for my taste. What does it mean "numerically solve" or the "right numeric method" for (a) an integral with one variable and with fixed limits, (b) for the above integral (on a compact domain in $Bbb R^3$)? Why is the usual approach to solve integral after integral after integral, each integral numerically computed "with usual algorithms", not applicable?
– dan_fulea
Nov 24 at 0:41
The question is not clearly delimited / defined for my taste. What does it mean "numerically solve" or the "right numeric method" for (a) an integral with one variable and with fixed limits, (b) for the above integral (on a compact domain in $Bbb R^3$)? Why is the usual approach to solve integral after integral after integral, each integral numerically computed "with usual algorithms", not applicable?
– dan_fulea
Nov 24 at 0:41
Well then the answer might be just easier. What algorithm can I use without using a symbolic library? I can't just code a regular algorithm with those limits.
– Cliff
Nov 24 at 0:45
Well then the answer might be just easier. What algorithm can I use without using a symbolic library? I can't just code a regular algorithm with those limits.
– Cliff
Nov 24 at 0:45
Simple algorithm (though not the best) to implement here is Monte Carlo integration. Make $n$ samples ${x,y,z}_i$ where you draw uniformly $xin[0,2]$ and $y,zin[0,16]$. Sum up $4xyz$ for the samples that satisfy $z<y$ and $x<y<8x$. Your integral is then this sum times $(16cdot 16cdot 2)/n$. The answer to $1%$ with $10^6$ samples.
– Winther
Nov 24 at 0:49
Simple algorithm (though not the best) to implement here is Monte Carlo integration. Make $n$ samples ${x,y,z}_i$ where you draw uniformly $xin[0,2]$ and $y,zin[0,16]$. Sum up $4xyz$ for the samples that satisfy $z<y$ and $x<y<8x$. Your integral is then this sum times $(16cdot 16cdot 2)/n$. The answer to $1%$ with $10^6$ samples.
– Winther
Nov 24 at 0:49
|
show 3 more comments
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python + scipy?
– Mark McClure
Nov 24 at 0:33
That's the second part! I need to be able to do it myself with a numeric method, then the computer.
– Cliff
Nov 24 at 0:34
The question is not clearly delimited / defined for my taste. What does it mean "numerically solve" or the "right numeric method" for (a) an integral with one variable and with fixed limits, (b) for the above integral (on a compact domain in $Bbb R^3$)? Why is the usual approach to solve integral after integral after integral, each integral numerically computed "with usual algorithms", not applicable?
– dan_fulea
Nov 24 at 0:41
Well then the answer might be just easier. What algorithm can I use without using a symbolic library? I can't just code a regular algorithm with those limits.
– Cliff
Nov 24 at 0:45
Simple algorithm (though not the best) to implement here is Monte Carlo integration. Make $n$ samples ${x,y,z}_i$ where you draw uniformly $xin[0,2]$ and $y,zin[0,16]$. Sum up $4xyz$ for the samples that satisfy $z<y$ and $x<y<8x$. Your integral is then this sum times $(16cdot 16cdot 2)/n$. The answer to $1%$ with $10^6$ samples.
– Winther
Nov 24 at 0:49