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Areas bounded by curves. Work diagrams

—The area enclosed between two different curves. Let PABQ and PA B Q (Fig. 103) be two curves, it is required to find the area PABQB A1. Let yl = fx(x) be the equation of one curve, y2 = f2(x), the equation of the other. First find the abscissae of the points of intersection of the two curves. Find separately the [Pg.237]

To find the area of the portion ABB Alet xl be the abscissa of AB and x2 the abscissa of BS, then, [Pg.238]

In illustration let us consider the area included between the two parabolas whose equations are y2 = Ax and x2 = 4y. The curves obviously meet at the origin, and at the point x = 4, cm., say, y = 4 cm. (16), page 95. Consequently, [Pg.238]

Let a given volume, x, of a gas be contained in a cylindrical vessel in which a tightly fitting piston can be made to slide (Fig. [Pg.238]

Let the sectional area of X the piston be unity. Now let the volume of. gas change dx units when a slight pressure X is applied to the free end of the piston. Then, by definition of work, W, [Pg.238]


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