# Evaluate! surface integral over surface

by ride4life
Tags: evaluate, integral, surface
 P: 428 Let me try ot reason through what you have. If at the end you were integrating dzdx, I'll assume I should try to paramet(e)rize the surface in x and z. Then r(x,z)=(x,2x^2,z). Then r_x=(1,4x,0), while r_z=(0,0,1). Then cross product is (r_x)x(r_z)=(4x,-1,0). Then the infinitesimal area on the surface is given by dS=sqrt(16x^2+1)dxdz. Now we want to integrate the SCALAR G(x,y,z)=4x against the area. That is, integrate G dS. So $\int_{x=0}^5\int_{z=0}^54x\sqrt{16x^2+1}\ dzdx.$ So my first guess is, you are mixing up VECTOR integrals with SCALAR integrals. You might compare them and their derivations.