What is the arclength of f ( x ) = arctan &#x2061;<!-- ⁡ --> (

Carlie Fernandez

Carlie Fernandez

Answered question

2022-05-20

What is the arclength of f ( x ) = arctan ( 2 x ) x on x [ 2 , 3 ]?

Answer & Explanation

Elbrinidr

Elbrinidr

Beginner2022-05-21Added 9 answers

Differentiaitng
f ( x ) = arctan ( 2 x ) x with respect to x
we get
f ( x ) = 2 x ( 1 + 4 x 2 ) arctan ( 2 x ) x 2
so we have to solve the integral
2 3 1 + ( 2 x ( 1 + 4 x 2 ) arctan ( 2 x ) x 2 ) 2 d x 1.01941

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