Practice question · Multiple choice
The Jacobian appears as a multiplying factor in every change of variables. What would go wrong if it were omitted?
Hints
- Ask how much area a small square in occupies after the map.
- In polar coordinates the factor is , why does it grow with radius?
Show the answer
B. The integral would count volume in the wrong units
Why
The Jacobian converts into real area. Omitting it weights every region equally when the map does not, which is why appears in polar and in spherical.
Practise Change of Variables and the Jacobian
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