Let K contained in R^n be a compact and connected set having boundary of volume zero. Let A be an open superset of K, and let T: A-> R^n where T is differentiable with continuous first partial derivatives. T is injective on the interior of K and the determinant of the Jacobian matrix for T is not zero on the interior of K. Let f: T(K)-> R be continuous.
Then
Integral of f over T(K) = Integral over k of f composed with T times the absolute value of the determinant of the Jacobian matrix for T.
I thought maybe typing it out here would help me remember it. I hear people talk about writing essays on Tumblr so it feels more like playtime.
I think maybe I was wrong in thinking that I could extend the function of math studying by zero over the internet box to prove that it is integrable.
Math is the corrupter.
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