What is the arclength of f ( x ) = x <mrow class="MJX-TeXAtom-ORD"> 2

Brice Colon

Brice Colon

Answered question

2022-05-23

What is the arclength of f ( x ) = x 2 e 1 x on x [ 1 , 2 ]?

Answer & Explanation

tatovihd1

tatovihd1

Beginner2022-05-24Added 6 answers

We are using the Formula
a b 1 + ( f ( x ) ) 2 d x
Calculating f'(x)
f ( x ) = 2 x e 1 x + x 2 e 1 x ( 1 x 2 )
simplifying we get
f ( x ) = e 1 x ( 2 x 1 )
so we have to compute
1 2 1 + ( e 1 x ( 2 x 1 ) ) 2 d x
This integral can not expressed by the known elementary functions.
By a numerical method we get 16.4316

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