Evaluate ∫C F · ds where f(x,y,z)=z and c(t)=(tcos(t),tsin(t),t) for 0<t<t0?
I know this should be easy be its my last problem and i keep coming up stumped!
Update:yes i meant to put ∫C f · ds...sorry
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1st : you have a F and an f , the F appears to be a vector valued function if the ' dot ' with the ds is to be a dot product...in which case I would take F = < 0 , 0 , z > and ds = < dx , dy , dz > , doing the product is just t dt , with a trivial integration
on the other hand if it was to be zds { no vectors } then you can easily see that ds = √ ( 2 + t²) dt , and again t ds is an easy integration....(1/3) [ (2 + to²) ^(1.5) - 2^(1.5) ]