Triple Integral w/ Respect to x & y Help

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The discussion revolves around interpreting the triple integral expression $$\int \frac{d^{3} x}{y^{3}}$$ and whether it represents the integral of "y" with respect to "x." Participants emphasize the need for additional context, such as bounds and whether "y" is a function of position in three dimensions, to fully understand the expression. The notation ##d^3x## is clarified as shorthand for multiple variables, indicating that there isn't a single variable "x" involved. Without more information, the expression remains ambiguous and cannot be accurately evaluated. Context is essential for meaningful interpretation of the integral.
NODARman
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Homework Statement
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Relevant Equations
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Hi, just wondering does this mean the triple integral of "y" with respect to "x"?
$$
\int \frac{d^{3} x}{y^{3}} .
$$
 
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Without the benefit of the context, I would say a cautious "yes". Cautious because ##d^3x## is shorthand for ##dx_1~dx_2~dx_3## so there is no single variable of integration "x".
 
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NODARman said:
Homework Statement:: .
Relevant Equations:: .

Hi, just wondering does this mean the triple integral of "y" with respect to "x"?
$$
\int \frac{d^{3} x}{y^{3}} .
$$
any context? bounds ? Complete problem statement ?
 
Is y a function of position in three dimensions?
 
BvU said:
any context? bounds ? Complete problem statement ?
haruspex said:
Is y a function of position in three dimensions?
I found it in a textbook, it's very general "equation".
 
NODARman said:
I found it in a textbook, it's very general "equation".
What you posted is an expression, not an equation. What is the rest of it?
There must be some context or it would be meaningless.
 

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