Find the arc length of the curve defined by $\vec { r } ( t ) = \langle 1 + \cos ( 3 t ) , 1 + \sin ( 3 t ) , 2 \rangle$ over $[ 1,5 ]$

Name: Find the arc length of the curve defined by $\vec { r } ( t ) = \langle 1 + \cos ( 3 t ) , 1 + \sin ( 3 t ) , 2 \rangle$ over $[ 1,5 ]$
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The Answer of Find the arc length of the curve defined by $\vec { r } ( t ) = \langle 1 + \cos ( 3 t ) , 1 + \sin ( 3 t ) , 2 \rangle$ over $[ 1,5 ]$

Find the Arc Length of the Curve Defined By r⃗(t)=⟨1+cos⁡(3t),1+sin⁡(3t),2⟩\vec { r } ( t ) = \langle 1 + \cos ( 3 t ) , 1 + \sin ( 3 t ) , 2 \rangler(t)=⟨1+cos(3t),1+sin(3t),2⟩

Find the Arc Length of the Curve Defined By $\vec { r } ( t ) = \langle 1 + \cos ( 3 t ) , 1 + \sin ( 3 t ) , 2 \rangle$