Articles liés à Examples in the Integral Calculus
Présentation de l'éditeur
In the differential calculus, we have to find the rates, or differentials, of given functions. In the integral calculus, having given any differential, we have to determine the function of which this is the rate; this function is called the integral of the given differential. The integral sign is i ;it is always written before an expression for a rate, the rate being generally expressed by a single variable and its differential; as, a dx f: which means that function of xwhose rate is a dx. 2. A definite integral is written with a number or letter, denoting a special value of the independent variable, at the bottom, and another at the top of the integral sign (these letters or numbers being called limits); thus, 3x dx and indicates the amount by which a quantity, varying with the rate under the integral sign, actually varies while the independent variable passes from the lower to the upper limitT hus, the above expression denotes the increment received by any quantity which has the rate a dx while xincreases from 1to3. 3. An indefinite integral is simply a variable which varies with the rate expressed under the integral sign, and is written without limits; thus, a dx pI twill be seen that the definite integral may, then, be defined as the increment received by the indefinite integral while Xpasses from the lower to the upper limit.
(Typographical errors above are due to OCR software and don't occur in the book.)
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