Steve,
The term 'area under the curve' is specifically used to look at the torque measurement on an engine to compare 2 cars that are both geared to use their respective rpm ranges, the one that makes more torque, makes a lot more power, and thus, all else equal, will be much much quicker.
f you have two hypothetical cars, and one makes an average of 200 ft-lb of torque from 2000 rpm to 4000 rpm and other makes 200 ft-lb of torque from 4000 rpm to 6000 rpm then clearly the second car will be quicker as it has a greater 'area under the curve'.
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