Find the length of the curve. r(t) = < 6t, t^2, 1/9(t^3) > , 0 <= t <= 1

BertonCO5

BertonCO5

Answered question

2022-12-03

Find the length of the curve. r ( t ) =< 6 t , t 2 , 1 9 ( t 3 ) > , 0 t 1

Answer & Explanation

Monserrat Wong

Monserrat Wong

Beginner2022-12-04Added 7 answers

Explanation:
r ( t ) =< 6 t , t 2 , 1 9 ( t 3 ) >
Then,
x ( t ) = d d t ( 6 t ) = 6 ( 1 ) = 6 y ( t ) = d d t ( t 2 ) = 2 2 1 2 t
And,
z ( t ) = d d t ( 1 9 ( t 3 ) ) = 1 9 ( 3 t 3 1 ) = 1 9 ( 3 t 2 ) = 1 3 ( t 2 )
Now calculating length of the given curve from 0 to 1,
L = 0 1 ( 6 ) 2 + ( 2 t ) 2 + ( 1 3 ( t 2 ) ) 2 d t = 0 1 ( 6 ) 2 + 2.6 1 3 ( t 2 ) + ( 1 3 ( t 2 ) ) 2 d t = 0 1 ( 6 + 1 3 ( t 2 ) ) 2 d t = 0 1 6 d t + 0 1 1 3 ( t 2 ) d t = 6 [ t ] 0 1 + 1 3 [ t 2 + 1 2 + 1 ] 0 1 = 6 [ 1 0 ] + 1 3 [ t 3 3 ] 0 1 = 6 + 1 3 [ 1 3 0 ] = 6 + 1 9 = 54 + 1 9 = 55 9
AimettiA8J

AimettiA8J

Beginner2022-12-05Added 1 answers

good

Do you have a similar question?

Recalculate according to your conditions!

New Questions in Elementary geometry

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?