   Chapter 12.5, Problem 3E

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# Finding the Arc Length of a Plane CurveIn Exercises 3–8, sketch the plane curve and find its length over the given interval. r ( t ) = t 3 i + t 2 j ,         [ 0 , 1 ]

To determine

To calculate: The plane curve and find the length over the interval [0, 1].

Explanation

Given:

The provided plane curve and the interval are shown below:

r(t)=t3.i^+t2.j^   [0, 1]

Graph: The couple of evaluations for this vector function are shown below,

r(0)=0.i^+0.j^ , r(0.2)=0.008i^+0.04j^ , r(0.4)=0.064i^+0.16j^ , r(0.6)=0.216i^+0.36j^ , r(0.8)=0.512i^+0.64j^ , r(1)=i^+j^ ,

Therefore, from the above evaluations following points are all on the graph of this vector function in the interval [0, 1].

(0,0),(0.008,0.04),(0.064,0.16),(0.216,0.36),(0.512,0.64),(1,1)

Plane curve over the interval is given below.

In this sketch included many more evaluations as calculated above

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