Multivariable Calculus Question?
Compute arclength of r(t) ( sin(t) ) 0 < or = t = or < 5
-------------------------------------( cos(t) )
-------------------------------------( t/2 )
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L = integral (from 0 to 5) [sqrt((dx/dt)^2 + (dy/dt)^2 + (dz/dt)^2 ) dt]
= integral (from 0 to 5) [sqrt((cos t)^2 + (- sin t)^2 + (1/2)^2 ) dt]
= integral (from 0 to 5) [sqrt((cos^2 t) + (sin^2 t) + 1/4 ) dt]
= integral (from 0 to 5) [sqrt(1 + 1/4 ) dt]
= integral (from 0 to 5) [sqrt(5/4) dt]
= integral (from 0 to 5) [ sqrt(5)/2 dt]
= ( sqrt(5)/2 )t [evaluated at 5 - evaluated at 0]
= ( sqrt(5)/2 )(5) - ( sqrt(5)/2 )(0)
= [5sqrt(5)]/2
[or (5/2)sqrt(5) ]