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#46
07 Á¡ÃÒ¤Á 2008, 21:54
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Íѹ¹Õéà»ç¹ à©Å ¢éÍ 2 µÍ¹ 2 ÍաẺ¤ÃѺ áµè¡çÂѧãªé Tchebyshev theorem ÍÂÙè´Õ (ºÃ÷ѴÅèÒ§ÊØ´ àÅ¢ 1 ËÅѧà¤Ã×èͧËÁÒÂź Áѹµ¡¢Íºä»¹Ð¤ÃѺ)
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#47
06 ÁÕ¹Ò¤Á 2008, 15:45
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¾Õè passer-by ¤ÃѺ¤ÓµÍº¢Í§¢éÍ 5.3 ¹Õèãªè $\displaystyle{\frac{11}{6}\pi^{2}+2\ln^{2}2}$ ËÃ×Íà»ÅèÒ¤ÃѺ
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$$\int_{0}^{\frac{\pi}{2}}\frac{a\cos x-b\sin x}{a\sin x+b\cos x}dx=\ln\left(\frac{a}{b}\right)$$ BUT $$\int_{0}^{\frac{\pi}{2}}\frac{a\cos x+b\sin x}{a\sin x+b\cos x}dx=\frac{\pi ab}{a^{2}+b^{2}}+\frac{a^{2}-b^{2}}{a^{2}+b^{2}}\ln\left(\frac{a}{b}\right)$$
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#49
06 ÁÕ¹Ò¤Á 2008, 21:06
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$$\int_{0}^{\frac{\pi}{2}}\frac{a\cos x-b\sin x}{a\sin x+b\cos x}dx=\ln\left(\frac{a}{b}\right)$$ BUT $$\int_{0}^{\frac{\pi}{2}}\frac{a\cos x+b\sin x}{a\sin x+b\cos x}dx=\frac{\pi ab}{a^{2}+b^{2}}+\frac{a^{2}-b^{2}}{a^{2}+b^{2}}\ln\left(\frac{a}{b}\right)$$
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#50
07 ÁÕ¹Ò¤Á 2008, 00:13
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#51
21 ÁÕ¹Ò¤Á 2008, 11:49
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#52
24 ÁÕ¹Ò¤Á 2008, 19:02
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$$\int_{0}^{\frac{\pi}{2}}\frac{a\cos x-b\sin x}{a\sin x+b\cos x}dx=\ln\left(\frac{a}{b}\right)$$ BUT $$\int_{0}^{\frac{\pi}{2}}\frac{a\cos x+b\sin x}{a\sin x+b\cos x}dx=\frac{\pi ab}{a^{2}+b^{2}}+\frac{a^{2}-b^{2}}{a^{2}+b^{2}}\ln\left(\frac{a}{b}\right)$$
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| ¢éÍÊͺ¤Ñ´µÑÇ Olympiad ÊÊÇ·. 2545 | ToT | ¢éÍÊͺâÍÅÔÁ»Ô¡ | 33 | 28 ¾ÄȨԡÒ¹ 2007 18:04 |
| Vietnam Mathematical Olympiad 2005 problem 4 | gools | ¢éÍÊͺâÍÅÔÁ»Ô¡ | 8 | 18 ÁԶعÒ¹ 2005 21:09 |
| The First POSN-Mathematical Olympiad | Rovers | ¢èÒǤÃÒÇáǴǧ Á.»ÅÒ | 4 | 06 ¾ÄÉÀÒ¤Á 2005 09:55 |
| The First POSN-Mathematical Olympiad | Rovers | »ÑËÒ¤³ÔµÈÒʵÃì·ÑèÇä» | 1 | 24 àÁÉÒ¹ 2005 02:12 |
| British Mathematical Olympiad | Tony | »ÑËÒ¤³ÔµÈÒʵÃì·ÑèÇä» | 14 | 15 àÁÉÒ¹ 2005 08:59 |
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