The Elements of the Integral Calculus; With Its Applications to Geometry And to the Summation of Infinite Series. Intended for the Use of Mathematical Students in Schools And Universities
The Elements of the Integral Calculus; With Its Applications to Geometry And to the Summation of Infinite Series. Intended for the Use of Mathematical Students in Schools And Universities
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In our eReader you can find the full English version of the book. Read The Elements of the Integral Calculus; With Its Applications to Geometry And to the Summation of Infinite Series. Intended for the Use of Mathematical Students in Schools And Universities 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 The Elements of the Integral Calculus; With Its Applications to Geometry And to the Summation of Infinite Series. Intended for the Use of Mathematical Students in Schools And Universities
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To quickly assess the difficulty of the text, read a short excerpt:
To determine the area of the catenary.
In this curve we have found (ex. 10, p, 1 17,) that a 2 = 2ax + x 2 , from which we get, by solving the quadratic, 8(k x =z x /o a + « a — a.\ dx = —-= = r v or — tr also, since universally we have dy == >/ d& — o , o = — = .... (1)- * v a 2 + a 2 ^/o 2 + ** Multiplying this by the value of r, above, we have a*ds xdy = ads — — ===== = ads — ady \f a* + s 9 .-. u ^fxdy = afds — afdy = as — ay . . . . (2), which requires no correction, since, *, y, and ti va...nish together. The area here found is that below the curve (see Jig. at p. 117) included between the tangent through the vertex, the ordinate at the extremity of *, and $ itself. Subtracting then this area from the rectangle xy = y Va* + s* — ay, we have « = y Va* + #» — a*, or since, by integrating (1), « + 1/ «• + «» .-. u = a ^o' + «Mog. LZ-ULJLL — at . . . . (4), a the area above the curve.
Digitized by Google THE INTEGRAL CALCULUS. 129 By putting in (3) for V& + s 2 its value a + x, above, and for * its value given by the first equation, it becomes , a + x + V 2ax + x 2 y = a log.
What to read after The Elements of the Integral Calculus; With Its Applications to Geometry And to the Summation of Infinite Series. Intended for the Use of Mathematical Students in Schools And Universities?
You can find similar books in the "Read Also" column, or choose other free books by J R John Radford Young to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
To determine the area of the catenary.
In this curve we have found (ex. 10, p, 1 17,) that a 2 = 2ax + x 2 , from which we get, by solving the quadratic, 8(k x =z x /o a + « a — a.\ dx = —-= = r v or — tr also, since universally we have dy == >/ d& — o , o = — = .... (1)- * v a 2 + a 2 ^/o 2 + ** Multiplying this by the value of r, above, we have a*ds xdy = ads — — ===== = ads — ady \f a* + s 9 .-. u ^fxdy = afds — afdy = as — ay . . . . (2), which requires no correction, since, *, y, and ti va...nish together. The area here found is that below the curve (see Jig. at p. 117) included between the tangent through the vertex, the ordinate at the extremity of *, and $ itself. Subtracting then this area from the rectangle xy = y Va* + s* — ay, we have « = y Va* + #» — a*, or since, by integrating (1), « + 1/ «• + «» .-. u = a ^o' + «Mog. LZ-ULJLL — at . . . . (4), a the area above the curve.
Digitized by Google THE INTEGRAL CALCULUS. 129 By putting in (3) for V& + s 2 its value a + x, above, and for * its value given by the first equation, it becomes , a + x + V 2ax + x 2 y = a log.
What to read after The Elements of the Integral Calculus; With Its Applications to Geometry And to the Summation of Infinite Series. Intended for the Use of Mathematical Students in Schools And Universities?
You can find similar books in the "Read Also" column, or choose other free books by J R John Radford Young to read onlineMoreLess
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