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Assume that s(t) and s'(t) are both continuous on [a,b]. If s(t) is measured in feet and t is measured in pounds, find the units of
To find the units of the integral, we multiply the units of the integrand and the units of the variable of integration.
(a) The units of are
(units of s)(units of t) = feet × pounds = foot-pounds.
Unlike wombat-meters, foot-pounds are a valid unit of measurement. A foot-pound measures the amount of work it takes to move one pound a distance of one foot.
(b) The units of are
The shorter way to do this problem is to remember that when you integrate the rate of change of s, the units are the same as the units of s.