 | Daniel Alexander Murray - Calculus - 1908 - 522 pages
...B FIG. 111. Note 5. Precautions to be taken in finding areas and computing integrals* Suppose that the area bounded by the curve y = f(x) , the xaxis, and the ordinates at A and B for which x = a and x = b respectively, is required. If the curve has an infinite ordinate... | |
 | Edward Vermilye Huntington, Louis Albert Fischer - Engineering - 1916 - 196 pages
.... . . жп), find the value of the function /(ж) at each of these points, and multiply it by Дж, the width of the interval ; then take the limit of...Geometrically, Ja f(x)dx is the area bounded by the curve у = Дж), the ж-axis, and the ordinates x = a and ж = b (Fig. 8) ; that is, briefly, the "area... | |
 | Mechanical engineering - 1916 - 1826 pages
...**, . . . x»), find the value of the function /(x) at each of these points, and multiply it by Ax, the width of the interval; then take the limit of...each individual term approaches zero. Geometrically, J^ f(x)dx is the area bounded by the curve y — /(x), the x-axis, and the ordinates x = a and x =... | |
 | Lionel Simeon Marks - Mechanical engineering - 1916 - 1922 pages
...it, . . . x»), find the value of the function /(x) at each of these points, and multiply it by Дх, the width of the interval; then take the limit of...each individual term approaches zero. Geometrically, Jf /(x)dx is the area bounded by the curve у = /(x), the x-axis, and the ordinates x = a and x = b... | |
 | Clyde Elton Love - Calculus - 1916 - 380 pages
...to b is Cb •X the definite integral I f(x)dx. \sa FIG. 57 Hence : Xb f(x)dx may be interpreted as the area bounded by the curve y =f(x), the x-axis, and the lines x = a, x = 6. EXERCISES 1. Find the area bounded by the parabola y2 = 4 ax, the z-axis, and the... | |
 | Herman William March, Henry Charles Wolff - Calculus - 1917 - 386 pages
...matter what other meaning it may have, it can always be regarded as representing the area included by the curve y — f(x], the X-axis, and the ordinates x = a and x = b, provided that f(x) is a function which can be represented by a continuous curve. This fact, that... | |
 | Joseph Lipka - Engineering - 1918 - 284 pages
...problems it is necessary to determine the value of the X& f(x) dx. Geometrically, this integral represents the area bounded by the curve y = f(x), the x-axis, and the ordinates x = a and x = b. Physically, it may represent the work done by an engine, the velocity acquired by a moving body,... | |
 | Joseph Lipka - Engineering - 1918 - 288 pages
...determine the value of the definite integral, / f(x) dx. Geometrically, this integral represents the «/o area bounded by the curve y — f(x), the x-axis, and the ordinates x = a and x = b. Physically, it may represent the work done by an engine, the velocity acquired by a moving body,... | |
 | Joseph Lipka - Engineering - 1918 - 284 pages
...Rectangular, Trapezoidal, Simpson's, and Durand's rules. — Suppose we wish to find the approximate area bounded by the curve y — f(x), the x-axis, and the ordinates x = x0 and x = xn (Fig. 101). 225 We divide the interval from x = x0 to x = xn into n equal intervals... | |
 | Frank Ward Sterling - Marine engineering - 1920 - 1522 pages
...X2, . . . x«), find the value of the function /(x) at each of these points, and multiply it by Ax, the width of the interval; then take the limit of...the number of terms increases indefinitely, while Fio. 2. each individual term approaches zero. Geometrically, Jt f(x)dx is the area bounded by the curve... | |
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Дx, the width of the interval ; then take the limit of the sum of the terms thus formed, when the number of terms increases indefinitely, while each individual term approaches zero. 
