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For questions that (at least in part) are specific to the United States of America.

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In a typical 3rd-semester multivariate calculus course in the US, what kind of area integral...

How about learning to manipulate the formula $$\int_S\|\partial_v\times\partial_w\|dv\wedge dw$$ for students of vector calculus? They, then, could be able calculate the area of the sphere, toroid, el …
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