Evaluate the surface integral. S(x + y + z) dS, S is the parallelogram with parametric equations
x = u + v, y = u − v, z = 1 + 2u + v, 0 ≤ u ≤ 7, 0 ≤ v ≤ 3.

Step-by-step explanation:

∫∫ ( x + y + z ) ds

where :

x = u + v ,  y = u - v ,  z = 1 + 2u + v ,  

0 ≤ u ≤ 5,  

0 ≤ v ≤ 1

R ( u,v ) = < u+v , u-v , 1 + 2u +v >   next we have to differentiate

attached below is a detailed solution

it is a reproduction.

step-by-step explanation:

answer: 0

step-by-step explanation: the positive, like 5, + its opposite, like -5 would be 0

5+(-5)=0, or 5-5=0