The place of the elementary calculus in the senior high-school mathematics : and suggestions for a modern presentation of the subject . Fig. 4 Fig. 5 If the divisions of the surface are parallel, and if x is the abscissaand y is the ordinate, the differential of the surface will be ydx;namely, the rectangle formed bythe ordinate and the differentialof the abscissa. If A C is the givencurve, then y will have a givenratio to x, so that it is expressedin x alone. Suppose that A C is aparabola, then ax = y2 or y =\/(ax). The integral of this, whichis y$x V (ax) or ^3 xy, is the areadesired. This m
The place of the elementary calculus in the senior high-school mathematics : and suggestions for a modern presentation of the subject . Fig. 4 Fig. 5 If the divisions of the surface are parallel, and if x is the abscissaand y is the ordinate, the differential of the surface will be ydx;namely, the rectangle formed bythe ordinate and the differentialof the abscissa. If A C is the givencurve, then y will have a givenratio to x, so that it is expressedin x alone. Suppose that A C is aparabola, then ax = y2 or y =\/(ax). The integral of this, whichis y$x V (ax) or ^3 xy, is the areadesired. This method of Bernoullis for fig. 6 finding the area is simple. It is also satisfactory, although the idea of limits involved is taken careof largely by intuition. This is a justification for the use of this. 28 Elementary Calculus in Senior High-School Mathematics
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