Elements of the Integral Calculus : With a Key to the Solution of Differential Equations
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In our eReader you can find the full English version of the book. Read Elements of the Integral Calculus : With a Key to the Solution of Differential Equations Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book Elements of the Integral Calculus : With a Key to the Solution of Differential Equations
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To quickly assess the difficulty of the text, read a short excerpt:
(3) Jo Joz For, in the second one, which agrees best with the figure, we must take our limits so that the limit of the sum of the projec- tions may be the quadi-ant in which the sphere is cut by the Chap. XI.] AEEAS OF SURFACES.
125 plane XZ ; and the equation of this section is obtained hj letting 2/ = in the equation of the sphere, and is whence z = Va^ — af.
If we take as our limits in the integral ( - clz zero and -s/ar— x^ ^ y we shall get the area whose projection is a strip running from ...the axis of Z to the curve ; then, taking j ( j - f^ ) f?^ from to a, we shall get the area whose projection is the sum of all these strips, and that is om- required surface.
y = Va^_a;2.
(T=al I — Jo Jo Va^ -x'-z^ f clz Vci^ — 3Cp — = sin"-^ - Vcr — af if we regard x as constant ; c7o- >/rt2-a;2 dz cr — a \ -ax = — , Jo 2 2 the required area. Formulas (1) and (3) give the same result.
133. Suppose two cylinders of revolution drawn tangent to each other, and perpendicular to the plane of a great circle of a sphere, each having the radius of the great circle as a diameter ; required the surface of the sphere not included by the cylinders.
What to read after Elements of the Integral Calculus : With a Key to the Solution of Differential Equations?
You can find similar books in the "Read Also" column, or choose other free books by Byerly, William Elwood, B. 1849 to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
(3) Jo Joz For, in the second one, which agrees best with the figure, we must take our limits so that the limit of the sum of the projec- tions may be the quadi-ant in which the sphere is cut by the Chap. XI.] AEEAS OF SURFACES.
125 plane XZ ; and the equation of this section is obtained hj letting 2/ = in the equation of the sphere, and is whence z = Va^ — af.
If we take as our limits in the integral ( - clz zero and -s/ar— x^ ^ y we shall get the area whose projection is a strip running from ...the axis of Z to the curve ; then, taking j ( j - f^ ) f?^ from to a, we shall get the area whose projection is the sum of all these strips, and that is om- required surface.
y = Va^_a;2.
(T=al I — Jo Jo Va^ -x'-z^ f clz Vci^ — 3Cp — = sin"-^ - Vcr — af if we regard x as constant ; c7o- >/rt2-a;2 dz cr — a \ -ax = — , Jo 2 2 the required area. Formulas (1) and (3) give the same result.
133. Suppose two cylinders of revolution drawn tangent to each other, and perpendicular to the plane of a great circle of a sphere, each having the radius of the great circle as a diameter ; required the surface of the sphere not included by the cylinders.
What to read after Elements of the Integral Calculus : With a Key to the Solution of Differential Equations?
You can find similar books in the "Read Also" column, or choose other free books by Byerly, William Elwood, B. 1849 to read onlineMoreLess
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