An Elementary Treatise On Variable Quantities, in Two Parts: the Direct And Inverse
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In our eReader you can find the full English version of the book. Read An Elementary Treatise On Variable Quantities, in Two Parts: the Direct And Inverse 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 An Elementary Treatise On Variable Quantities, in Two Parts: the Direct And Inverse
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70. There can be only one rate of a given function, but there may be more than one function answering to a given rate. This is obvious, since x'^ and x'^ -\- a have the same rate, viz., 2xdx. Therefore, in integrating, a constant term must be added to the integral. This term is usually represented by C ; thus the integral of du = 2axdx is u^^ax -\- C.
C is called an arbitrary constant, and the integral before the value of C is known is called an incomplete integral. In the solution of a real pr...oblem, however, the value of C may be determined from the known conditions of the problem and consequently a complete integral obtained.
For illustration take the ratal equation of the straight line, dy = adx, whence y=^ax-\-C.
If the straight line passes through the origin of the coordi- nates, then y = when x = 0; hence C ^ 0, and the complete or true integral is y = ax.
102 AN ELEMENTARY TREATISE But if the straight line cuts the axis of ordinates at a dis- tance from the origin equal to b, then for x = 0, y = b, conse- quently C = b, and the true integral is y^ ax -{- b.
What to read after An Elementary Treatise On Variable Quantities, in Two Parts: the Direct And Inverse?
You can find similar books in the "Read Also" column, or choose other free books by Cook, Hiram, 1827-1917 to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
70. There can be only one rate of a given function, but there may be more than one function answering to a given rate. This is obvious, since x'^ and x'^ -\- a have the same rate, viz., 2xdx. Therefore, in integrating, a constant term must be added to the integral. This term is usually represented by C ; thus the integral of du = 2axdx is u^^ax -\- C.
C is called an arbitrary constant, and the integral before the value of C is known is called an incomplete integral. In the solution of a real pr...oblem, however, the value of C may be determined from the known conditions of the problem and consequently a complete integral obtained.
For illustration take the ratal equation of the straight line, dy = adx, whence y=^ax-\-C.
If the straight line passes through the origin of the coordi- nates, then y = when x = 0; hence C ^ 0, and the complete or true integral is y = ax.
102 AN ELEMENTARY TREATISE But if the straight line cuts the axis of ordinates at a dis- tance from the origin equal to b, then for x = 0, y = b, conse- quently C = b, and the true integral is y^ ax -{- b.
What to read after An Elementary Treatise On Variable Quantities, in Two Parts: the Direct And Inverse?
You can find similar books in the "Read Also" column, or choose other free books by Cook, Hiram, 1827-1917 to read onlineMoreLess
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