How do you find the arc length of x = 2 3 </mfrac> ( y &#x2212;<!-- − -->

skottyrottenmf

skottyrottenmf

Answered question

2022-05-21

How do you find the arc length of x = 2 3 ( y 1 ) 3 2 between 1 y 4?

Answer & Explanation

Madisyn Avery

Madisyn Avery

Beginner2022-05-22Added 12 answers

It can be found by L = 0 4 1 + ( d x d y ) 2 d y
Let us evaluate the above definite integral.
By differentiating with respect to y,
d x d y = ( y 1 ) 1 2
So, the integrand can be simplified as
1 + ( d x d y ) 2 = 1 + [ ( y 1 ) 1 2 ] 2 = y = y 1 2
Finally, we have
L = 0 4 y 1 2 d y = [ 2 3 y 3 2 ] 0 4 = 2 3 ( 4 ) 3 2 2 3 ( 0 ) 3 2 = 16 3
Hence, the arc length is 16 3

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