Given (t)=4sinti+at+4 costi find the arc length for t € [0,*]. What is the formula for arc length in 3D space: Fedt dt [*Folde dt Fede dt *F (1) ² dt
Given (t)=4sinti+at+4 costi find the arc length for t € [0,*]. What is the formula for arc length in 3D space: Fedt dt [*Folde dt Fede dt *F (1) ² dt
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.2: Graphs Of Equations
Problem 46E
Related questions
Question
![Given(t)=4sinti+atj+4 costi find the arc length for t € [0,*].
What is the formula for arc length in 3D space:
*** de
dt
□
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Step-By-Step Example
What is the value of r(t):
"Fol:
["Folde
dt
[F(t)\ dt
(1) dt
Answer format: Enter a number
I
Live Help](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc167378a-6772-4355-bdb0-a5fec1af8d0e%2F46fd9c53-1ed1-4022-a8f2-93329ecfe205%2Fq1jmo7c_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Given(t)=4sinti+atj+4 costi find the arc length for t € [0,*].
What is the formula for arc length in 3D space:
*** de
dt
□
Congratulations! your answer is correct (and saved).
Check Answer/Save
Step-By-Step Example
What is the value of r(t):
"Fol:
["Folde
dt
[F(t)\ dt
(1) dt
Answer format: Enter a number
I
Live Help
![Check Answer/Save
Solution: L=
STEP-BY-STEP EXAMPLE
Given F(t) = 2 costi +tj +2 sintk find the arc length fort € [0, π].
= [*F(0)|d
dt
7 (t) = -2 sinti+3+2 costk
F(t)² = (- 2 sint)² + (1)² + (2 cost)² = 4 sin² t +1+4 cos² t = 4(sin²t + cos² t) + 1= 41+1=5
So L=
Step-By-Step Example
0
1/² √5 dt = √5]
Fod
(t) dt = √5
Arc length is:
Live Help
dt =
= √5lt = √5(T-0) = √5
What is the arc length of (t) ft [0, :
X
Answer format: Enter the value [for sign, type \pi or use the calculator]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc167378a-6772-4355-bdb0-a5fec1af8d0e%2F46fd9c53-1ed1-4022-a8f2-93329ecfe205%2Fu25bl3n_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Check Answer/Save
Solution: L=
STEP-BY-STEP EXAMPLE
Given F(t) = 2 costi +tj +2 sintk find the arc length fort € [0, π].
= [*F(0)|d
dt
7 (t) = -2 sinti+3+2 costk
F(t)² = (- 2 sint)² + (1)² + (2 cost)² = 4 sin² t +1+4 cos² t = 4(sin²t + cos² t) + 1= 41+1=5
So L=
Step-By-Step Example
0
1/² √5 dt = √5]
Fod
(t) dt = √5
Arc length is:
Live Help
dt =
= √5lt = √5(T-0) = √5
What is the arc length of (t) ft [0, :
X
Answer format: Enter the value [for sign, type \pi or use the calculator]
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