Distance or Arc Length

• $L=\int_a^b\sqrt{(\frac {dx} {dt})^2+(\frac {dy} {dt})^2}$

Displacement

• $\lang \int_a^b x'(t), \int_a^b y'(t)\rang$

Tips

When one $\frac {dy} {dt}$ or $\frac {dx} {dt}$ is not given, use the formula of $\frac {dy} {dx} =\frac {\frac {dy} {dt}}{\frac {dx} {dt}}$ and set the equation with $\frac {dy} {dx}$ to yield out the other derivative of $\frac {dy} {dt}$ or $\frac {dx} {dt}$