Answer:
12.5
Explanation:
[tex]r(t)=(1+2sint)i+(1+3sin^2t)j+(1+1sin^3t)k[/tex]
Work done by F can be found by calculating [tex]\int\limits_C F.dr[/tex].
[tex]W = \int(1+2sint,1+3sin^2t,1+1sin^3t).(2cost,6sint*cost,2sin^2t*cost)dt=[/tex]
[tex]=\int\limits^{\pi/2}_0 (2cost+2sin2t+3sin2t+18sin^3t*cost+2sin^2t*cost+2sin^5t*cost)dt=[/tex]
[tex]= -5cos^2t + 2sint + 2/3 sin^3t + 9/2 sin^4t + 1/3 sin^6t |_0^{\pi/2}=[/tex]
[tex]= 25/2 = 12.5[/tex]
