Find the area of the surface. the part of the cylinder y^2+z^2=9 that lies above the rectangle with vertices (0,,,2), and (4,2)

We can parameterize this part of the cylinder using



with and . Then the surface element is




so the area is given by the surface integral, where denotes the part of the cylinder in question,



Probably less work would involve a simpler geometric approach, but it doesn't hurt to practice setting up a proper surface integral.