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Reversing the order of integration

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To reverse the order of integration of $$\int_{x_\text{min}}^{x_\text{max}} \int_{y_\text{min}(x)}^{y_\text{max}(x)} f(x,y) dy dx,$$
  1. Sketch the two dimensional region of integration,
  2. Find the minimum and maximum values of $y$,
  3. For each $y$, find the minimum and maximum values of $x$,
  4. Rewrite the integral as $$\int_{y_\text{min}}^{y_\text{max}} \int_{x_\text{min}(y)}^{x_\text{max}(y)} f(x,y) dx dy$$
This is the same process as writing down an iterated integral.

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