Someone help. 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)=1. Find the line integral ∫∇f⋅dr ⃗ and explain your answer.

Question

amistre64 · Answer

can you write the integral out using the draw box or the equation tool?  hard to tell what [] is spose to mean

anonymous · Answer

Find the  line integral $$\int\limits_{a}^{b} ∇f⋅dr ⃗ $$

anonymous · Answer

@amistre64

amistre64 · Answer

that does look better :)

how far have you gotten so far? or what about the process are you stuck at?

anonymous · Answer

i am kind  of thinking of fundamental theorem of line integral but not sure about it

amistre64 · Answer

my first thought was stokes, but i am a bit rusty

anonymous · Answer

whatever help would be good. What do you think? I mean i have no idea so anything would be helpful.

amistre64 · Answer

my difficulty at the moment is try to interpret the information, it sounds very general.
$$f(x,y,z)=1$$
$$f_x=0~:~f_y=0~:~f_z=0$$
$$\nabla f=(f_x,f_y,f_z)=(0,0,0)$$
the dot product to this would just be 0,  so I would say that the integration is up to a variable: t

$$\int_{a}^{b} 0 ~dt=b-a$$

amistre64 · Answer

but then again, i am a it rusty and i cannot verify this to be correct

amistre64 · Answer

http://openstudy.com/study#/updates/52a528c7e4b0256dd0989f74 this person is asking the same question ... you may be able to help each other out.

anonymous · Answer

$$ f(x1,y1,z1) - f(xo, yo,zo) = 1-1= 0$$ that what i was thinking of .... using fundamental theorem.

anonymous · Answer

@amistre64 yeah we have exact same question.... hopefully i might get some help from him

amistre64 · Answer

good luck with it :)  if i come across anything that I can be sure about, I will let you know.

anonymous · Answer

@amistre64 thanks...