How do you find the distance travelled from t=0 to t=1 by a particle whose motion is given by #x=4(1-t)^(3/2), y=2t^(3/2)#?
You can integrate the speed of travel to get a distance of
The speed is the length of the velocity vector. It is equal to
We differentiate to get
The distance traveled is therefore
This integral can be done by the substitution
Now use the Fundamental Theorem of Calculus to get