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Chapter 11: Q. 22 (page 889)

Find the arc length of the curves defined by the vector-valued functions on the specified intervals in Exercises 22鈥�27.

r(t)=鉄�3t-4,-2t+5,t+3鉄�,[1,5]

Short Answer

Expert verified

The length is414.

Step by step solution

01

Step 1. Given information.

The given vector-valued function isr(t)=鉄�3t-4,-2t+5,t+3鉄�on[1,5].

02

Step 2. Arc length.

The arc-length of the curve is given by,

I(a,b)=鈭�abr'(t)dtr'(t)=(3)2+(-2)2+(1)2=14Therefore,(l)=鈭�abr'(t)dt=鈭�1514dt=14t]15=14(5-1)=414

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