What is the arc length of f ( x ) = e <mrow class="MJX-TeXAtom-ORD"> 3

crossoverman9b

crossoverman9b

Answered question

2022-06-14

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

Answer & Explanation

lilao8x

lilao8x

Beginner2022-06-15Added 22 answers

The arc length s of the curve f on x [ a , b ] is given by
s = a b 1 + ( f ( x ) ) 2 d x
Here, f ( x ) = e 3 x + x 2 e x s o f ( x ) = 3 e 2 x + 2 x e x + x 2 e x . The arc length is then:
s = 1 2 1 + ( 3 e 2 x + 2 x e x + x 2 e x ) 2 d x
s 97.6

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