Page Description Equation
arclength of a curve $y=f\left(x\right)$ on the interval $[a, b]$ and $L$ is the arclength. \[ L=\int_a^b \sqrt{1+\left(\frac{dy}{dx}\right)^2}\dx \]
arclength of a parametric curve $(x,y)=\left(f(t),g(t)\right)$ on the interval $I=[a,b],$ where $f:I\stackrel{\text{1-1}}{\rightarrow}\R,$ $g:I\stackrel{\text{1-1}}{\rightarrow}\R,$ $f'(t)$ and $g'(t)$ are continuous and nonzero on $I,$ and $L$ is the length. \[ L=\int_a^b \sqrt{ \left(\frac{dx}{dt}\right)^2 +\left(\frac{dy}{dt}\right)^2 }\dt \]