ok sounds good. just a short quick push on flux if u can answer. I am supposed to do the double int to the surface s of vector f dot n. can i do that with respect to the t or do i have to change it all the way back to x and y
ok i ended up getting 2sint+3cost the next little problem though is over that interval i get 0. should i just take the it from 0 to pi and multiply it by 2?
okay i got that part now the greens thrm one. my book only has it in terms of x and y but i have a feeling itd be easier using the R(t) one. the best it describes it is to do the integral of -pi to pi of F(r(t))dotr'(t) dt but i do not understand wat it fully means by the F(r(t)).
H(x,y)=<x^2/4,y^2/9,xy> the region E is 9x^2+4y^2<=36
also wat is given is the work is counterclockwise on R=<2cost,3sint> from -pi<=t<=pi
wat the questions are what is the unit tangent the outward normal vector with respect to the region E in terms of t. for the unit tangent i think its...
alright i did it all the way through and got E(z)=z E(y)=y and E(x)=x because that's the only difference in the equations once i get down to that point for each of them so would my answer then be x+y+z+xy^2z^3 or is my logic off completely on the E's?
ok so i did that and then set the whole thing to df/dy and got the c(z)=z. so do i just keep doing that all the way thru to get c(y) and C(x) and just throw that on the end? the part that's really throwing me off is the 1+stuff. i guess I am a little more confused then i thought i was.
Homework Statement
find the potential function of the vector field F(x,y,z0=<1+y^2z^3,1+2xyz^3,1+3xy^2z^2>
Homework Equations
The Attempt at a Solution
for some reason i can't figure out what to do with the third point.
i took the integrals of each point and got
integral(1+y^2z^3)...