## Length of Curve Formula Proof

The length of a section of curve between the points
$(x,y), \: (x+dx, y+dy)$
is from Pythagoras theorem,
$dl=\sqrt{(dx)^2+(dy)^2}=\sqrt{1+(\frac{dy}{dx})^2}dx$
.
The length of the curve from
$x=a$
to
$x=b$
is then just the integral of this.
$L=\int^b_a \sqrt{1+(\frac{dy}{dx})^2}dx$
.