15.3 Surface Integrals: Surface Area and Flux

1. Evaluate where and is that part of the plane which is located in the first octant.

Sol) .

2. If is the entire surface of the cube bounded by , , , , , and and then evaluate .

Sol)

Therefore .

3. Let be the surface of the cylinder included in the first octant between and . Evaluate where .

Sol)

,

,

,

Therefore .

4. Find the surface integral over the parallelepiped , , , , , when .

Sol)

,

,

,

,

,

.

Therefore .

5. If is the surface of the sphere and , evaluate .

,

6. Evaluate .

Here and is the boundary of the solid surrounded by and .

Sol)

1) :

.

2) : .

3) : .