Woods, Frederick S. (Frederick Shenstone), 1864-, Bailey, Frederick H. (Frederick Harold), 1865- · Boston, New York [etc.] Ginn and Company · leaf 393
transform (3) of § 174 into I (x^-x^dy, (3) which will represent the same area that is represented by (2),(.r2 — x^) dy being the area of the rectangle AB CD. It is evident that, if the areabounded by a plane curve expressedin rectangular coordinates is foundby double integration, the result ofthe… … Accordingly we let y1 = x + 3 — V-i — x2and y2 = x + 3 + V4 — x2, whence y„ — y1 = 2 V4 — x2, and take for theelement of area a rectangle such as ABCD. Its area is 2 V4 — x2dx. Since the curve is bounded by the lines x = — 2 and x = 2, — 2 and 2are the limits of integration. Hence the area = ( 2 v4…
Geometry, Analytic · Calculus
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