Study guide and 1 practice problem on:

## Reversing the order of integration

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.