What is the arc length of f(x)=2-3x on

Kenley Wagner

Kenley Wagner

Answered question

2022-05-20

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

Answer & Explanation

Norah Baxter

Norah Baxter

Beginner2022-05-21Added 10 answers

f'(x)=-3
d L = 1 + ( f ( x ) ) 2 d x
= 1 + ( 3 ) 2 d x
= 10 d x
L = 2 1 10 d x
= 3 10
Alternatively, since this is a straight line, we can use Pythagoras' Theorem.
The horizontal is 1-(-2)=3 units
The vertical is f(1)-f(-2)=(-1)-11=-12 units.
Using Pythagoras' Theorem, we have the length of the diagonal as
3 2 + 12 2 = 3 10

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