Calculate Line Integral for a Function on a Level Surface | Homework Equations

[joemama69]

Homework Statement

Let f(x,y,z) be a function of three variables. Suppose that C is an oriented curve lying on the level surface f(x,y,z) = 5. Find the integral grad f dot dr.

Homework Equations

The Attempt at a Solution

integral grad f dot dr = integral f(q) - f(p)

not sure what to do

 

[dx]

If a point p is on the level surface f(x,y,z) = 5, what does that tell you about f(p)?

 

[gabbagabbahey]

If the curve you are integrating over lies on the surface f(x,y,z)=5, then surely the endpoints p and q do as well right?...So f(p)=___? and f(q)=___?

 

[joemama69]

f(P) - f(Q) = 5 - 5 = 0

 

[joemama69]

is that correct

 

[dx]

It's correct.

 

[AUMathTutor]

If f(x,y,z) = 5, how is grad f not equal to (0,0,0)? Jeez, today's just not my day.

 

[dx]

f(x,y,z) = 5 on the level surface, not everywhere. If it was equal to 5 everywhere, grad f would be zero.

 

[AUMathTutor]

Oh yeah, duh. I think I need to drink more water or something.