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 22–27.
$r (t) = ⟨ 3 t - 4, - 2 t + 5, t + 3 ⟩, [1, 5]$

Short Answer

Expert verified

The length is $4 \sqrt{14} .$

Step by step solution

Step 1. Given information.

The given vector-valued function is $r (t) = ⟨ 3 t - 4, - 2 t + 5, t + 3 ⟩ o n [1, 5] .$

Step 2. Arc length.

The arc-length of the curve is given by,

$I (a, b) = \int_{a}^{b} ||r^{'} (t)|| d t ||r^{'} (t)|| = \sqrt{(3)^{2} + (- 2)^{2} + (1)^{2}} = \sqrt{14} T h e r e f o r e, (l) = \int_{a}^{b} ||r^{'} (t)|| d t = \int_{1}^{5} \sqrt{14} d t = \sqrt{14} t]_{1}^{5} = \sqrt{14} (5 - 1) = 4 \sqrt{14}$

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Find the arc length of the curves defined by the vector-valued functions on the specified intervals in Exercises 22–27.
$r (t) = ⟨ 3 t - 4, - 2 t + 5, t + 3 ⟩, [1, 5]$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Arc length.

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Find the arc length of the curves defined by the vector-valued functions on the specified intervals in Exercises 22–27.r(t)=⟨3t-4,-2t+5,t+3⟩,[1,5]

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Arc length.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Applied Mathematics

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Study anywhere. Anytime. Across all devices.

Find the arc length of the curves defined by the vector-valued functions on the specified intervals in Exercises 22–27.
$r (t) = ⟨ 3 t - 4, - 2 t + 5, t + 3 ⟩, [1, 5]$