- #1

- 3

- 0

## Homework Statement

Verify Stokes' theorem

∫

_{c}F •

**t**

*ds*= ∫∫

_{s}

**n ∇ ×**F

*dS*

in each of the following cases:

(a) F=

**i**z

^{2}+

**j**y

^{2}

C, the square of side 1 lying in the x,z-plane and directed as shown

S, the five squares S

_{1}, S

_{2}, S

_{3}, S

_{4}, S

_{5}as shown in the figure.

(b) F =

**i**y +

**j**z +

**k**x

C, the three quarter circle arcs C

_{1}, C

_{2}, and C

_{3}directed as shown in the figure.

S, the octant of the sphere x

^{2}+ y

_{2}+ z

_{2}= 1 enclosed by the three arcs.

(c) F =

**i**y -

**j**x +

**k**z

C, the circle of radius R lying in the xy-plae, centered at (0,0,0) and directed as shown in the figure.

S, the curved upper surfaces of the cylinder of radius R and height h.

## Homework Equations

∫

_{c}F •

**t**

*ds*= ∫∫

_{s}

**n ∇ ×**F

*dS*Stokes' theorem

## The Attempt at a Solution

I have been staring at this problem for two weeks and every time I think i get it, i find out I'm wrong. Please help!