Evaluate the surface integral. s xz ds s is the boundary of the region enclosed by the cylinder y2 + z2 = 25 and the planes x = 0 and x + y = 10

Split up the surface into three sub-surfaces , where:

(1) is the part of in the plane parameterized by



with and ;

(2) is the part of in the plane parameterized by



with and ; and

(3) is the part of on the cylinder parameterized by



with and .

In each respective case, we get surface elements





So the surface integral is



The first integral is



The second is



The third is



and so