## Length of Curve Formula Proof

\[(x,y), \: (x+dx, y+dy)\]

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.\[L=\int^b_a \sqrt{1+(\frac{dy}{dx})^2}dx\]

.