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

1 Answer
Jan 26, 2016

3sqrt10

Explanation:

f'(x) = -3

dL = sqrt{1 + (f'(x))^2} dx

= sqrt{1 + (-3)^2} dx

= sqrt{10} dx

L = int_{-2}^1 sqrt{10} dx

= 3sqrt{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

sqrt{3^2+12^2} = 3sqrt10