11-sinf Matematika 2-qism

© “ZAMIN NASHR” MCHJ, 2018 © Barcha huquqlar himoyalangan Algebra va analiz asoslari bo‘limining mualliflari: M.A. Mirzaahmedov, Sh.N. Ismailov, A.Q. Amanov Geometriya bo‘limining muallifi: B.Q. Xaydarov UO‘K: 51(075.32) KBK: 22.1ya72 M 54 Taqrizchilar: R.B. Beshimov – Mirzo Ulug‘bek nomidagi O‘zbekiston Milliy Universiteti “Geometriya va topologiya” kafedrasi mudiri, fizika-matematika fanlari doktori; Q.S. Jumaniyozov – Nizomiy nomidagi TDPU fizika- matematika fakulteti “Matematika o‘qitish metodikasi” kafedrasi dotsenti, pedagogika fanlari nomzodi; R.O. Ro‘zimov – Sergeli tumani 237- umumta’lim maktabi matematika fani o‘qituvchisi; S.B. Jumaniyozova – RTM metodisti; I.B. Saibova – Yashnobo…

3 Algebra va analiz asoslari II BOB. INTEGRAL VA UNING TATBIQLARI 47–50 ANIQ INTEGRALNING TATBIQLARI Yuzlarni integrallar yordamida hisoblash Masala. Rasmdagi ABCD shakl yuzi S hisoblansin (7.a-rasm). 7.a-rasm.  Ravshanki, bu shaklning S yuzi aBCb va aADb egri chiziqli trapetsiyalar yuzlarining ayirma­ siga teng: ( ) 2 1 2 1 ( ) ( ) ( ) ( ) . b b b a a a S f x dx f x dx f x f x dx = − = − ∫ ∫ ∫ (1) Javob: ( ) 2 1 ( ) ( ) . b a S f x f x dx = − ∫ ▲ (1) formula 2 1 ( ) ( ) f x f x ≥ shartni qanoatlantiradigan uzluksiz funksiyalar uchun to‘g‘ridir. 1-misol. y=x to‘g‘ri chiziq va y=x2+2x–2 parabola bilan chegaralangan shakl yuzini hisoblang.  1) y=x va y=x2+2x–2 chiziqlarning kesishish nuqtala…

4 ( ) 1 1 3 2 2 2 2 2 1 7 10 ( 2 2) ( 2) ( 2 ) ( ) 4,5. 2 3 2 6 3 x x S x x x dx x x dx x − − = − + − = − − + = − − + = −− = − ∫ ∫ Javob: S=4,5 (kv.birlik). ▲ 9-rasm. 2-misol. y x = va 2 y x = chiziqlar bilan chegaralangan shakl yuzini hisoblang.  [0;1] x∈ kesmada 2 x x ≤ (9-rasm). (1) formulada a=0, b=1, 2 1( ) , f x x = 2( ) f x x = deymiz. U holda 3 1 2 3 2 0 1 2 1 2 1 1 ( ) ( ) (kv.birlik) 0 3 3 3 3 3 S x x dx x x = − = − = − = ∫ . Javob: 1 kv.birlik. 3 S = ▲ Aylanish jismlarining hajmini hisoblash 10-rasm. Egri chiziqli trapetsiyani Ox o‘qi atrofida aylantirish natijasida hosil bo‘ladigan jismning hajmi 2( ) b a V f x dx π = ⋅∫ p (2) formula bilan hisoblanishini isbotlash mumkin. Bu fo…