MHB Help With Calculus Question: Finding Value of F(r(t))

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The discussion revolves around a calculus question from a Stewart textbook, specifically regarding the evaluation of F(r(t)). The user initially presents their solution involving an integral from 0 to 2π, but expresses uncertainty about its correctness. They seek clarification on whether their approach is valid and what the correct value of F(r(t)) should be. Ultimately, the user resolves their issue, indicating that they found the solution. The conversation highlights the importance of verifying calculations in calculus problems.
Kris1
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Hi,

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.
 
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