- #1
Minusu
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Homework Statement
Find the length of the curve traced by the given vector function on the indicated interval.
r(t)=<t, tcost, tsint> ; 0<t<pi
Homework Equations
s= ∫||r'(t)||dt
The Attempt at a Solution
r'(t) = <1, -tsint + cost, tcost + sint>
s= ∫||r'(t)||dt
||r'(t)|| = sqrt(1^2+(-tsint+cost)^2+(tcost+sint)^2)
||r'(t)|| = sqrt(1+t^2sin^2t-2tsintcost+cos^2t+t^2cos^t+2tsintcost+sin^2t)
||r'(t)|| = sqrt(1 + t^2sin^2t+t^2cos^2t+sin^2t+cos^2t)
I'm not sure where to go from here. I was thinking of using the trig identity sin^2x+cos^2x= 1, but I don't think I can do that.