(See Solution) Change the order of integration in the following integrals: ∫_0^2(∫_x^2 x f(x, y) d y) d x; ∫_0^1(∫_x^4^x^2 f(x, y) d y) d x;


Question: Change the order of integration in the following integrals:

  1. \(\int_{0}^{2}\left(\int_{x}^{2 x} f(x, y) \mathrm{d} y\right) \mathrm{d} x\);
  2. \(\int_{0}^{1}\left(\int_{x^{4}}^{x^{2}} f(x, y) \mathrm{d} y\right) \mathrm{d} x\);
  3. \(\int_{1}^{e}\left(\int_{0}^{\ln (x)} f(x, y) \mathrm{d} y\right) \mathrm{d} x\)

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