3.1: Double Integrals
- Page ID
- 191925
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- Find the area of planar regions bounded by curves using double integrals.
- Be able to switch the order of integration in a double integral.
- Use double integrals to determine the signed volume under a surface.
The concept of integration is the natural progression after differentiation. In the same vein as taking partial derivatives by treating all other variables as constants, we review how to take integrals of multivariable functions. We discuss applications of iterated or double integrals for finding areas of two dimensional domains, and extend this to finding volumes of three dimensional regions under surfaces defined by multivariable functions. We define Type I and Type II regions and how to integrate real valued functions over them, as well as how to switch between them when necessary.