. Applied calculus; principles and applications . efinitely. 259 260 INTEGRAL CALCULUS It is easily seen that the difference between the sum of therectangles as formed and the area A is less than a rectanglewhose base is Ax and whose altitude is a constant, / (6) —/ (a). Since this difference approaches zero as Ax = 0. thesum of either set of rectangles approaches the area A as a 0 M^ M^ M^ M^ M^ M^X limit. It is evident that the sum of the rectangles whichare partly above the curve is greater than A, while the sumof those which are wholly under the curve is less than A.By the notation of a su

GLIX-115-2CGGPWM

. Applied calculus; principles and applications . efinitely. 259 260 INTEGRAL CALCULUS It is easily seen that the difference between the sum of therectangles as formed and the area A is less than a rectanglewhose base is Ax and whose altitude is a constant, / (6) —/ (a). Since this difference approaches zero as Ax = 0. thesum of either set of rectangles approaches the area A as a 0 M^ M^ M^ M^ M^ M^X limit. It is evident that the sum of the rectangles whichare partly above the curve is greater than A, while the sumof those which are wholly under the curve is less than A.By the notation of a su
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. Applied calculus; principles and applications . efinitely. 259 260 INTEGRAL CALCULUS It is easily seen that the difference between the sum of therectangles as formed and the area A is less than a rectanglewhose base is Ax and whose altitude is a constant, / (6) —/ (a). Since this difference approaches zero as Ax = 0. thesum of either set of rectangles approaches the area A as a 0 M^ M^ M^ M^ M^ M^X limit. It is evident that the sum of the rectangles whichare partly above the curve is greater than A, while the sumof those which are wholly under the curve is less than A.By the notation of a su

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