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i) r(t) = cos t i + sin t j [pi/2 <=t<= 3pi/2]

ii) r(t) = 2t i + j [0<=t<=1]

for i):

F(r (t) ) = - sin t i + cos t j

r'(t) = - sin t i + cos t j

integ F(r(t)) dot r'(t) dt

= integ 1 dt [pi/2<=t<= 3pi/2]

so integral is

3pi/2 - pi/2 = pi ???

is this correct so far.