   Chapter 13.3, Problem 7E

Chapter
Section
Textbook Problem

# Find the length of the curve correct to four decimal places. (Use a calculator to approximate the integral.)7. r(t) = ⟨t2, t3, t4⟩, 0 ≤ t ≤ 2

To determine

To find: The length of the curve L for the vector equation r(t)=t2,t3,t4,0t2 .

Explanation

Given data:

r(t)=t2,t3,t4,0t2

Formula used:

Write the expression to find length of the curve L for the vector r(t) .

L=ab|r(t)|dt (1)

Here,

r(t) is the tangent vector, which is the derivative of vector r(t) , and

[a,b] is parameter interval.

Find the tangent vector r(t) .

r(t)=ddt[r(t)]

Substitute t2,t3,t4 for r(t) ,

r(t)=ddtt2,t3,t4

r(t)=ddt(t2),ddt(t3),ddt(t4) (2)

Write the following formula to compute the expression for r(t) .

ddt(t2)=2tddt(t3)=3t2ddt(t4)=4t3

Apply the corresponding formula in equation (2) to find r(t)

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