Chapter 14.6, Problem 71E

Special case of surface integrals of scalar-valued functions Suppose that a surface S is defined as z = g(x, y) on a region R. Show that t_x × t_y = 〈–z_x, –z_y, 1〉 and that ${\displaystyle {\iint }_{S}f\left(x,y,z\right)dS=}{\displaystyle {\iint }_{R}f\left(s,y,g\left(x,y\right)\right)}\sqrt{z_x^2+z_y^2+1}dA$.