   Chapter 13.3, Problem 8E

Chapter
Section
Textbook Problem

# Find the length of the curve correct to four decimal places. (Use a calculator to approximate the integral.)8. r(t) = ⟨t, e−t, te−t⟩, 1 ≤ t ≤ 3

To determine

To find: The length of the curve L for the vector equation r(t)=t,et,tet,1t3 .

Explanation

Given data:

r(t)=t,et,tet,1t3

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 t,et,tet for r(t) .

r(t)=ddtt,et,tet

r(t)=ddt(t),ddt(et),ddt(tet) (2)

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

ddt(t)=1ddt(et)=etddt(tet)=ettet

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

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