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Answers for “在三重积分中,$dV$ 总是等于 $dx \, dy \, dz$ 吗?”

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No, dVdV is not always equal to dx dy dzdx \, dy \, dz. In Cartesian coordinates, dV=dx dy dzdV = dx \, dy \, dz, but in other coordinate systems, such as cylindrical or spherical coordinates, the expression for dVdV changes to account for the geometry of the coordinate grid.

Conditions: The current setup uses rectangular/Cartesian coordinates.; In other coordinate systems, such as polar-type coordinates mentioned verbally, dVdV may take a different form.