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- W1509845731 abstract "In this short paper, I introduce an elementary method for exactly evaluating the definite integrals $, int_0^{pi}{ln{(sin{theta})},dtheta}$, $int_0^{pi/2}{ln{(sin{theta})},dtheta}$, $int_0^{pi/2}{ln{(cos{theta})},dtheta}$, and $int_0^{pi/2}{ln{(tan{theta})},dtheta} ,$ in finite terms. The method consists in to manipulate the sums obtained from the logarithm of certain products of trigonometric functions at rational multiples of $pi$, putting them in the form of Riemann sums. As this method does not involve any search for primitives, it represents a good alternative to more involved integration techniques. As a bonus, I show how to apply the method for easily evaluating $,int_0^1{ln{Gamma(x)} , d x}$." @default.
- W1509845731 created "2016-06-24" @default.
- W1509845731 creator A5057374410 @default.
- W1509845731 date "2009-09-03" @default.
- W1509845731 modified "2023-09-27" @default.
- W1509845731 title "A shortcut for evaluating some definite integrals from products and limits" @default.
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- W1509845731 hasPublicationYear "2009" @default.
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