arc length 6.3
Remark :if f' does not exist,then we may be able to write the equation y=f(x) as
x = g(y) and use the formula
ﬁnd the length of the curve
Alternatively,we may write
work and ﬂuid forces 6.5
If a body moved a distance d along a straight line as a result of being acted on by
a constant force F, then we deﬁne the workW done by the force,asW=F d.
Often,the work describes the "change in energy" of the body.
If F is in Newtons (N),and d is in meters (m),thenW is in Newton-meter (N m),
or in joules (J).
If F is in pounds (lb) and d is in feet (ft),thenW is in foot-pound(ft lb). Example
if a force of 100 lb is used to pull a cart 200 ft,then the work done by the force is
If a variable force F(x) is causing an object to move from x=a to x=b,then the
work can be approximated by a Riemann Sum