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អាំងតេក្រាល

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092774440

092774440 អាំងតេក្រាល x រ ៀបរ ៀងរោយ ៖ ធែល សេងថុង 200 2 3 sin x 2 1cos (1 2cos x) រយើងរោោះស្រាយអំងរតព្កាលខាងរលើរោយបរ ូ អរេ ាង រយើងបាៃ ែូចរៃោះ u cos x +របើ +របើ I ខ. ក្ចំៃួៃរិត 1 2 I រ x 2 x 3 រ ោះ រ du du sin xdx ោះ ោះ u 0 2 u u 0 1 1 2 1 2 du 1 u 2 1 2 u u u 0 1 1 1 2 a , b ៃិង c 1 ររមាៃ ដែលចំរ du dx u u u 0 1 1 1 2 ោះព្រប់ 1 u 0, 2 a b c 1 u 1 u 1 2u 1 u 1 u 1 2u ររទញបាៃ 2 1 1 2 1 1 2 1 1 a u u b u u c u u 1 u 1 u 1 2u 2 2a 2b cu 3a bu a b c 1 u1 u1 2u a b c1 1 3ab0 2 2a 2b c 0 3 1 , 3 2 1 4 b3a ជំៃួស ររបាៃ a c 8ac0 5 1 1 4 ាម 4 ៃិង 5 រយើងបាៃ a , b ៃិង c 6 2 3 4 1 1 1 4 ែូចរៃោះ ៃិង 3 1 u 1 u 1 2u 6 1 u 2 1 u 3 1 2u រ.រណ 1 1 a , b 6 2 អំងរតព្កាល I c ដែល 2 3 dx sin x sin 2x

092774440 អាំងតេក្រាល រយើងមាៃ I 2 3 ែូរចនោះ dx sin x sin 2x 2 3 ៨៥.រណ អំងរតព្កាល I a, b ចំរ ាង 1 2 du u u u 0 1 1 1 2 1 2 1 1 4 6 1 u 2 1 u 3 1 2u 0 du 1 1 2 ln 1 u ln 1 u ln 1 2u 6 2 3 1 1 1 3 2 ln ln ln 2 6 2 2 2 3 4 1 ln 2 ln 3 3 2 dx 4 1 ln 2 ln 3 sin x sin 2x 3 2 b dx a b x x a របើ a ៃិង b ជារី ចំៃួៃរិតដែល a b ោះកា រោោះស្រាយអំងរតព្កាល រៃោះ ររអចរោោះស្រាយរោយបរ ូ អរេ រី 2 t x a 1 b a +របើ x a រ ោះ រ ោះ t 1 I a, b b a x t 1 a 2 ំឲ្យ b a dx dt 2 1 2 0 ab , 1,1 រៅ ែូរចនោះ +របើ x b រ ោះ t 1 b a 1 dt 2 b a I a, b I 1,1 2 1 b a b a 1 t 1 t 2 2 +រណ I 1,1 -ចំរ ោះ ាង 1 1 ររបាៃ 1,1 1 1 dx 1 x 1 x 1 1 1 1 1 1 ដែល 1 x 1 x 1 1 x 1 1 x I dx dx dx 2x 2 x 2 x 1 x dx រោោះស្រាយរោយបរ x ូ អរេ u 1x រ ោះ dx 2udu I 1,1 1 1 dx 1 x 1 x +របើ x 1 រ ោះ 0 u រ ៀបរ ៀងរោយ ៖ ធែល សេងថុង 201

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