The vertical slices of a cone form arches. A curve can be divided into many little pieces, each of which is approximately straight. Arc lengths as integrals are usually evaluated using antiderivatives. 8.3 Applications to Physics 1. Work is only done if an object moves.
Time has nothing to do with work.
The work done to raise a bar of iron 1 meter on the surface of the moon is thesame as on the surface of the earth. What goes up must come down. Water pressure is proportional to depth. 8.5 Application to Distribution Functions 1. The distribution of the number of years of education completed by adults in a population is approximately by a formula.