Question

Evaluate the surface integral.

S is the triangular region with vertices (1, 0, 0), (0, - 2, 0), and (0, 0, 4)

Answer 1

Step 1 :

Surface integral .

Step 2 : 

Evaluate .

Let the three vertices of the region be .

Then,

,

,

Thus, the plane is .

Rewrite the plane as .

Step 3 :

.

Consider the domain as : .

Consider .

Apply partial derivatives with respect to x .

.

Consider .

Apply partial derivatives with respect to y .

.

Step 4 :

Now,

Thus, .

Solution :

.