Changing the Order of Integration in Double Integrals

Double integrals provide a practical method for determining the volume of liquid contained in tanks with irregularly shaped sides. To estimate the total volume, the base region of the tank is divided into many very small rectangular sections. Each section forms the base of a thin column of liquid, and the volumes of all these columns are added t...

Double integrals can be used to calculate the total volume of liquid contained in a tank with irregularly shaped sides.

To determine this volume mathematically, the base region of the tank is divided into many small rectangular columns, and the volumes of these columns are summed using a double integral.

The sides of the tank can be ...