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

length of a line