Question

Evaluate the surface integral.

S is the parallelogram with parametric equations x = u + v,

Answer 1

Step 1 :

If a smooth parametric surface S  is given by the equation

and S  is covered just once as ranges throughout the parameter domain D , then the surface area of S  is ,

where .

Step 2 :

Find .

The parametric equations are .

The domain is .

.

Step 3 :

.

Step 4 :

Thus, .

Solution :

.