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My question in my Stewart Calculus book is the same as

http://faculty.tru.ca/smcguinness/M317W11/M317W11quiz4sol.pdf

However when I work out the solution I seem to get a different value. My solution is

integral from 0 to 2pi 16 <2cos^2t,2sin^2t,cos(t)sin(t)>

64 integral from 0 to 2pi -cos^2t*sin(t)+sin^2t+cos(t)

I'm not sure however as to whether I am on the right track. Can someone show me what the value of F(r(t)) is and if my solution is on the right track?

Sorry about the formatting.