[15] (3) GIVEN: The space curve I parameterized by: c(t) = (e'sint, e' cost, e'), te[0, In 2] FIND: The length of I, L(r). (Remember to BOX your answer)
[15] (3) GIVEN: The space curve I parameterized by: c(t) = (e'sint, e' cost, e'), te[0, In 2] FIND: The length of I, L(r). (Remember to BOX your answer)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
Please please For the first image attached please do the calculations similar to the second image attached
![[15] (3) GIVEN: The space curve I parameterized by:
č(t) =
(2√2)1³), r=[0,1]
FIND: The length of I, L(r). (Remember to BOX your answer)
METHOD:
:Ĉ=Ĉ(t), t€ [a,b]
⇒ b(r) = f'll c´µ dt
a
ĉ = (tent, teint, ²√2 + ²)
⇒Ĉ'=(cort-tsint, Aint + + cost, √x + ²)
⇒||ĉ'|| ³² = (cat - taint) ²+ (aint + ±cat) ²+ 2 t
+2t
Colt-Haint coat + t²rin'²t
+ Ain't + 2t Aint colt + t² w₂²t
+ 2t
2
= 1+ t + 2t =
= t cost, tsint,
=
(t+1) ²
⇒ ||¢'′)) = | t+1) = t +1, \± € [0,1]
Hence, L(r) = √√²t+1dt
2
= [½/t²+t
-
=
32
Always
search for
the simplest
expression of
your answer.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9755e55f-b204-4ec5-8a10-7bbad16cf793%2Fa42f0aa5-b0aa-4052-b510-a91d131eebad%2Fdcs8fxg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:[15] (3) GIVEN: The space curve I parameterized by:
č(t) =
(2√2)1³), r=[0,1]
FIND: The length of I, L(r). (Remember to BOX your answer)
METHOD:
:Ĉ=Ĉ(t), t€ [a,b]
⇒ b(r) = f'll c´µ dt
a
ĉ = (tent, teint, ²√2 + ²)
⇒Ĉ'=(cort-tsint, Aint + + cost, √x + ²)
⇒||ĉ'|| ³² = (cat - taint) ²+ (aint + ±cat) ²+ 2 t
+2t
Colt-Haint coat + t²rin'²t
+ Ain't + 2t Aint colt + t² w₂²t
+ 2t
2
= 1+ t + 2t =
= t cost, tsint,
=
(t+1) ²
⇒ ||¢'′)) = | t+1) = t +1, \± € [0,1]
Hence, L(r) = √√²t+1dt
2
= [½/t²+t
-
=
32
Always
search for
the simplest
expression of
your answer.
![[15] (3) GIVEN: The space curve I parameterized by:
c(t) = (e'sint, e' cost, e'), t = [0, In 2]
FIND: The length of I, L(r). (Remember to BOX your answer)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9755e55f-b204-4ec5-8a10-7bbad16cf793%2Fa42f0aa5-b0aa-4052-b510-a91d131eebad%2Flbs5v3k_processed.jpeg&w=3840&q=75)
Transcribed Image Text:[15] (3) GIVEN: The space curve I parameterized by:
c(t) = (e'sint, e' cost, e'), t = [0, In 2]
FIND: The length of I, L(r). (Remember to BOX your answer)
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