Summary
Special case of Fubini’s theorem
Area of region
Surface area
Double integral in polar coordinates
Concept
Fubini’s theorem
- volume over a rectangle
Type I region
- bounded by functions of
- vertical arrow
Type II region
- bounded by functions of
- horizontal arrow
Area and surface area
Application
Evaluating iterated integral
order of integration does not matter
Factorizable function
Type I region
Converting between types/interchanging order
use the one that is easier to compute
Volume above xy-plane
find the domain first, then find the volume
Polar rectangles
Surface area of parabola
Slicing by planes