Evaluate the surface integral. (give your answer correct to at least three decimal places.) s is the boundary of the region enclosed by the cylinder x2 + z2 = 1 and the planes y = 0 and x + y = 2

Split up the surface into three main components , where

is the region in the plane bounded by ;

is the piece of the cylinder bounded between the two planes and ;

and is the part of the plane bounded by the cylinder .

These surfaces can be parameterized respectively by


where and ,


where and ,


where and .

The surface integral of a function along a surface parameterized by is given to be



Assuming we're just finding the area of the total surface , we take , and split up the total surface integral into integrals along each component surface. We have










Therefore

You can find it by multiplying the areas it show u