How do you find the arc length of the curve y = 4 x <mrow class="MJX-TeXAtom-ORD">

hornejada1c

hornejada1c

Answered question

2022-07-04

How do you find the arc length of the curve y = 4 x 3 2 1 from [4,9]?

Answer & Explanation

Elias Flores

Elias Flores

Beginner2022-07-05Added 24 answers

Arc length would be 4 9 ( 1 + ( d y d x ) 2 ) d x
= 4 9 ( 1 + 36 x ) d x
= [ 2 3 1 36 ( 1 + 36 x ) 3 2 ] 4 9
= 1 54 [ ( 343 ) 3 2 ( 145 ) 3 2 ]
= 1 54 [ 7 9 2 ( 145 ) 3 2 ]
This can be simplified, if required, to get an approximation, using calculator.
ScommaMaruj

ScommaMaruj

Beginner2022-07-06Added 5 answers

An error has crept into the solution. The correction is as follows:
Arc length = 1 54 [ ( 1 + 36 x ) 3 2 ] 4 9
= 1 54 [ 325 3 2 145 3 2 ]
This can be simplified, if required as 1 54 [ 5859.020 1746.031 ]
=76.1664

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