Given a vector equation, find the surface area

Question

Question:

r(u,v) = ucosv i + usinv j + v k  
for v and u, 0<=v<=7pi, 0<=u<=1  
Find the surface area. 

from Google I got these steps:

• Find derivative of r w.r.t. u (r_u) and derivative of r w.r.t. v (r_v)
• Find r_u x r_v (cross-product)
• Surface area = ∫∫ ||r_u x r_v|| dA

But I don't understand what is the real meaning(is it a tangent vector? But toward which direction?) of r_u and r_v. Also, where is the ∫∫ ||r_u x r_v|| dA from?

Thanks!