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The integral symbol is U+222B ∫ INTEGRAL in Unicode [5] and \int in LaTeX. In HTML , it is written as ∫ ( hexadecimal ), ∫ ( decimal ) and ∫ ( named entity ). The original IBM PC code page 437 character set included a couple of characters ⌠,⎮ and ⌡ (codes 244 and 245 respectively) to build the integral symbol.
A line integral (sometimes called a path integral) is an integral where the function to be integrated is evaluated along a curve. [42] Various different line integrals are in use. In the case of a closed curve it is also called a contour integral. The function to be integrated may be a scalar field or a vector field.
When the direction of a Euclidean vector is represented by an angle , this is the angle determined by the free vector (starting at the origin) and the positive -unit vector. The same concept may also be applied to lines in a Euclidean space, where the angle is that determined by a parallel to the given line through the origin and the positive x ...
The symbol was introduced originally in 1770 by Nicolas de Condorcet, who used it for a partial differential, and adopted for the partial derivative by Adrien-Marie Legendre in 1786. [3] It represents a specialized cursive type of the letter d , just as the integral sign originates as a specialized type of a long s (first used in print by ...
female sign u+2642: ♂: male sign u+2660: ♠: black spade suit u+2661 ♡ white heart suit u+2662 ♢ white diamond suit u+2663: ♣: black club suit u+266d ♭ music flat sign u+266e ♮ music natural sign u+266f ♯ music sharp sign
Integration is the basic operation in integral calculus.While differentiation has straightforward rules by which the derivative of a complicated function can be found by differentiating its simpler component functions, integration does not, so tables of known integrals are often useful.
A different technique, which goes back to Laplace (1812), [3] is the following. Let = =. Since the limits on s as y → ±∞ depend on the sign of x, it simplifies the calculation to use the fact that e −x 2 is an even function, and, therefore, the integral over all real numbers is just twice the integral from zero to infinity.
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