4. [0/1 Points] DETAILS PREVIOUS ANSWERS SCALCET8 13.3.503.XP. Reparametrize the curve with respect to arc length measured from the point where t = 0 in the direction of increasing t. (Enter your answer in terms of s.) r(t) = 2ti + (2 3m + (3 +4t)k Need Help? Submit Answer 5. [-l1 Points] DETAILS SCALCET8 13.3.504.XP. Reparametrize the curve with respect to arc length measured from the point where t = 0 in the direction of increasing t. (Enter your answer in terms of s.) r(t) = e4t cos(4t)i + 2j + e4t sin(4t)k r(115)) = Need Help? _ Reparametrization with respect to arc length measured from the point where t = 0 in the direction of increasing t. (Enter your answer in terms of s.) r(t) = e4t cos(4t) i + 2j + e4t sin(4t) k In In r(t(s)) = e V2 cos In i + 2 j+ e V2 sin In K XAt po(t ) ecos ( 42 ) 1+23 te sin (At ) k Differentiate win.t t n' ( t ) = ( felt cos ( At ) - 4 etsin ( at ) )it 0? + ( felt sin ( At ) + 4e ( cos( 4k ) ) ( felt ( coscat )- sin ( 48)4 ( felt ( sin(at ) +cos(4 ) Ibe bt cos ( 47 ) - 2 . cositsinat+ sin at ) + 1be' sin 94 2 ) + 2 sin 47 cos4t + cos At ) ) 16 e 16t 1 - 2 costsin At + 1 + 2 sing twosat)Now ; the clelength ? - s= sit ) = In'(u ) /1 du 2 Al v 2 du O t 2 AV2 6 Substitute Au = V dv = 4du u to dusav Vato 2 12V2 [evy At 0 2 . 12et so , In 4 + = In (s) - In(2 ) 4\f2 In(s ) - In (2 ) . In (12 ) 2 2 In ( 2 ) 12 2 -2 In ( 2 ) 2 2 In(s) - In(2) 8 Now smostitute i we get D'(t ( s ) ) 4 x 2 2n(s) - In(2) 2 e 8 Cos 4x 2ln(s )- In(2 ) 8 4x 2 ln(s )- In(2 ) + 2 3 + e Som/ 4x 20n(s )-In( 2 ) 8