Find the arc length of the curve on the given

jeliceg2

jeliceg2

Answered question

2021-12-04

Find the arc length of the curve on the given interval. Parametric Equations
x=t, y=3t1 Interval 0t1

Answer & Explanation

tnie54

tnie54

Beginner2021-12-05Added 18 answers

Step 1
Given:
Parametric Equations
x=t
y=3t1
Interval 0t1
Step 2
Explanation:
Formula:
Arc length expressed parametrically:
Arc length =abds
where
ds=( dx  dt )2+( dy  dt )2
Step 3
x=t
Differentiate in light of t
 dx  dt =12t
y=3t1
Differentiate with respect to t
 dy  dt =3
Interval t1
As a result, to calculate the arc length, use the above values in the formula
Step 4
Arc length =abds
Arc length =01( dx  dt )2+( dy  dt )2
Arc length =01(12t)2+(3)2dt
Arc length =0114t+9dt
Arc length =011+36t4tdt
Arc length =011+36t4tdt
Arc length =011+36t2tdt
Arc length =12011+36ttdt
Put u=6tdu=3t dt  dt =tdu3
and u2=36t
Put
t=0u=0
t=1u2=36u=6
Therefore,
Arc length =12061+u2t×tdu3
Arc length =16 

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