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Section 15.1: Double Integrals over rectangles

Exercise 52

  1. In what way are the theorems of Fubini and Clairaut similar?
  2. If \(f(x, y)\) is continuous on \([a, b] \times [c, d]\) and \(g(x, y) = \int_a^x \int_c^y f(s, t) dt ds\) for \(a < x < b, c < y < d\), show that \(g_{xy} = g_{yx} = f(x, y)\).