What is the arc length of f ( x ) = 3 x x −...

Zion Wheeler

Zion Wheeler

Answered

2022-06-24

What is the arc length of f ( x ) = 3 x x 1 on x [ 2 , 6 ]?

Answer & Explanation

enfujahl

enfujahl

Expert

2022-06-25Added 20 answers

Writing
f ( x ) = 3 x ( x 1 ) 1 2
then by the product and the chain rule we get
f ( x ) = 3 ( x 1 ) 1 2 + 3 x ( 1 2 ) ( x 1 ) 3 2
which simplifies to
f ( x ) = 3 ( x 2 ) 2 ( x 1 ) 3 2
so we have to solve
2 6 1 + ( 3 x 2 2 ( x 1 ) 3 2 ) 2 d x
by a numerical method we get
4.51

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