The modern notation for the definite integral, with limits above and below the integral sign, was first used by Joseph Fourier in " M�moires " of the French Academy around 1819 20, reprinted in his book of 1822 (; ).
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:: : See Lagrangian density for an integral over 4-dimensional spacetime ( though the article uses only a single integral sign with d 4 " x " )-- talk ) 22 : 41, 6 May 2014 ( UTC)
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Taking my origin at the center, I know that the x-coordinate of the COM should be ( 1 / M ) Sxdm ( i'm using capital s for my integral sign ) and similarly for the y-coordinate ( 1 / M ) Sydm.
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The example here is a minimal example of an issue that came up when I was thinking about the fundamental theorem of calculus and the more general formula for differentiation under the integral sign . & mdash; Carl ( talk ) 15 : 04, 27 April 2010 ( UTC)
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Therefore differentiation under the integral sign is easy to justify when ? > 0, but proving that the resulting formula remains valid when ? is 0 requires some careful work . " Unfortunately the article doesn't give a lot of clues about when differentiating under the integral sign is valid.
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Therefore differentiation under the integral sign is easy to justify when ? > 0, but proving that the resulting formula remains valid when ? is 0 requires some careful work . " Unfortunately the article doesn't give a lot of clues about when differentiating under the integral sign is valid.
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The function under the integral sign is not continuous at the point ( " x ", ? ) = ( 0, 0 ) and the function ? ( ? ) has a discontinuity at ? = 0, because ? ( ? ) approaches �� / 2 as ? ?! 0 ?
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Multiple integration of a function in variables : over a domain is most commonly represented by nested integral signs in the reverse order of execution ( the leftmost integral sign is computed last ), followed by the function and integrand arguments in proper order ( the integral with respect to the rightmost argument is computed last ).
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Multiple integration of a function in variables : over a domain is most commonly represented by nested integral signs in the reverse order of execution ( the leftmost integral sign is computed last ), followed by the function and integrand arguments in proper order ( the integral with respect to the rightmost argument is computed last ).
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In contrast, my math textbooks are very adamant about being clear about limits of integration, i . e . they would write no such thing as I = \ int r ^ 2 dm but instead \ iiint _ Q r ^ 2 dm or with one integral sign, \ int _ Q r ^ 2 dm .-- ( talk ) 10 : 24, 3 May 2014 ( UTC)
