The northern half a local beltway is a circle with a slowly varying offset:

The northern half a local beltway is a circle with a slowly varying offset: y=f(x) =√100−x2 + sin(π/10*x)

The origin is at the center of the city, x is the east-west distance to the center of the city and y is the north-south distance to the center. If one starts at x=-9 and goes to x=7 along the beltway, how far does one travel? Use whatever you like to help compute the length and graph the curve; there is no need to compute the derivative or arclength integral by hand-use our electronic tools. After that, try computing the length of the curve from the endpoints: x=-10 to x=10.What happens? Try to figure out why it is happening.