I started this question and got stuck;
Show that the differential form in the integral is exact. Then evaluate the integral:
Integral from (0,0,0) to (3,3,1) of 2xdx - y^2dy - 4/(1+z^2)dz
This is what I've done so far:
M=2x , N=-y^2 , P=-4/(1+z^2)
Then I showed that it is conservative because;
dp/dy=dn/dz , dm/dz=dp/dx , dn/dx=dm/dy
*(I wasn't sure what it meant by showing it was exact, I thought that meant conservative)*
from here I did;
df/dx=2x ---> f(x,y,z)=x^2 + g(y,z)
But then df/dy=x^2 + dg/dy = y^2 so this is where I didn't understand what to do....
Please help if you know this!!!