(a) A pin moves along a straight guide so that its velocity v(m/s) when it is a distance x(m)from the beginning of the guide at time t(s) is given in the table on the right. Use Simpson's rule with eight intervals to determine the approximate total distance traveled by the pin in the 4.0 s period.

Time t(s)	0	0.5	1.0	1.5	2.0	2.5	3.0	3.5	4.0
Velocity v (m/s)	0	0.052	0.082	0.125	0.162	0.175	0.186	0.160	0