5 Multiple Integrals

Consider a surface z = f (x,y). Let a line increment on the curve C in the xy plane be given by s.

y

z  yxfz , The area of the band formed from the line increment to the surface is given by the product:   syxf , The total area under the surface along the curve from P1 to P2 is thus the limit of the sum as s goes to zero.