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Application of line integral in an exercise


New member
May 8, 2016
Hello, can someone help me with this exercise ?

Compute the work done by the force field F(r, θ) = (−4sinθ, 4sinθ) (given inpolar coordinates) in moving a particle along the curve r = e[SUP]−θ[/SUP]from (1,0) to the origin.

I'm doing the line integral using the formula of the line integral so Work= ∫[SUB]c [/SUB]F · ds =∫[SUP]a[/SUP][SUB]b[/SUB] F(c(t)) · c'(t)dt
and I have ∫[SUP]1[/SUP][SUB]0[/SUB] (-4sin(t),4sin(t)) · (-4cos(t),4cos(t)) dt so now when I compute it I get 16 and the result should be 8/5

I would appreciate your help. Thanks in advance.