Thread: vector analysis integrals

question.

if F(x,y) = f(x,y)i + g(x,y)j
f and g are continuous on an open connected region D.

a) what can you say about the work integrals of F along paths in D if
F = del(phi ), for some function phi(x,y)?

b) what can you say about F and work integral of F along paths in D if fsuby=gsubx throughout D?
What assumptions must be made about D?

C) given F(x,y) = (e^y +ye^x )i +(xe^y +e^x) j.
Compute the integral of C F dot dr if C is the path from (0,0) to (1,0) that follows the spiral r = theta /4pi.

Thank you!

Originally Posted by universe09

question.

if F(x,y) = f(x,y)i + g(x,y)j
f and g are continuous on an open connected region D.

a) what can you say about the work integrals of F along paths in D if
F = del(phi ), for some function phi(x,y)?

b) what can you say about F and work integral of F along paths in D if fsuby=gsubx throughout D?
What assumptions must be made about D?

For (a) by using the fundamental theorem of line integrals you zero get zero.

For (b) by using Green's theorem you get the integral of 0 over D which is zero.