w Ss^ TRAN V I N H I hiet ke bai giang GIAI TICH ] TAP HAI mmT: f-'.i /-, ^ * ' r >'» c I'tl'l ^ N H A X U A T BAN H A N I TRAN VINH THIET KE BAI GIANG GIAI TICH TAP HAI NHA XUAT BAN HA NOI Chi/dNq III NGUYEN HAM - TICH PHAN VA UNC DUNG Phan NHJtXG VAX D E CUA CHMfONG I NOI DUNG Noi dung chinh cua chucung : Nguyen ham : Dinh nghia ; tinh chat; cac nguyen ham ccf ban ; cac phucmg phap tinh nguyen ham Tich phan : Dinh nghia ; cac tinh chat cua tich phan ; cac phuang phap tinh tich phan " Lftig dung cua tich phSn : Bai toan dien tich, bai toan thi tich n MUC TIEU Kien thiirc Nam dugc toan bo kien thiic co ban chuong da neu tren, cu the : Nam viing dinh nghia nguyen ham, cac nguyen ham co ban, cac tinh chat ciia nguyen ham • Dinh nghia tich phan, cac tinh chat ciia tich phan, ung dung ciia tich phan, moi quan he giiia tich phan va nguyen ham M6t s6' ling dung tich phan hinh hoc : Tinh dugc dien tich hinh phang, the tich vat the khong gian KT nang van dung cac nguyen ham co ban de tinh cac nguyen ham Van dung thao cong thiic Niuton - Laibonit de tinh tich phan Moi quan he giiia dao ham va nguyen ham Van dung tich phan de tinh dien tich hinh phang va the tich ciia vat the Thai Tu giac tich cue, dgc lap va chii dgng phat hien ciing nhu ITnh hoi kien" thiic qua trinh hoat dgng Cam nhan dugc su cSn thiet cua dao ham viec khao sat ham so Cam nhan dugc thuc te cua toan hgc, nhat la doi vdi dao ham P H a n CAC B A I SOA]!!^ §1 N g u y e n ham (tiet 1, 2, 3, 4, 5) I MUC TIEU Kien thurc HS nam duac : Nh6 lai each tinh dao ham cua ham sd • Dinh nghia nguyen ham • Cac tinh chat ciia nguyen ham Mot so' nguyen ham co ban Cac phuong phap tinh nguyen ham : Phuong phap doi bien sd va phuong phap nguyen ham tiing phan KT nang HS tinh thao cac nguyen ham co ban Tinh dugc nguyen ham dua vao phuong phap doi bien sd va phuong phap nguyen ham tiing phan Thai Tu giac, tich cue hgc tap Biet phan biet ro cac khai niem co ban va van dung tiing trudng hgp cu the " Tu cac va'n de cua toan hgc mot each Idgic va he thdng n C H U A N B I C U A G V VA H S Chuan bj ciia GV Chuan bi cac cau hoi ggi mo Chuan bi pha'n mau, va mdt sd dd diing khac Chuan bj cua HS Can dn lai mot sd kien thiic da hgc ve dao ham P H A N PHOI THCJI L U O N G Bai chia lam tiet: Tiet : Tic dau den hit miic phdn I Tiet : Tiep theo den het phdn I Tiet : Tiep theo den het muc I phdn II Tiet : Tiep theo den het phdn II Tiet : Bdi tap IV TIEN TRINH DAY HOC A DAT VAN OE Cau hoi Xet tinh diing - sai cua cac cau sau day : a) Ham sd y = In(cosx) cd dao ham y' = -tanx b) Ham sd y = In(cosx) cd dao ham y' = -cotx Cau hoi C h o h a m s d y = 3''"" a) Hay tinh dao ham cua ham sd da cho b) Chiing minh rang ham sd y = x3''"'' cd dao ham la y' = 3''"" GV: Ham y = xS^'"" ggi la nguyen ham ciia ham sd y' = 3^'"" B BAi Mdl I NGUYEN H A M VA TINH CHAT HOATDONC1 Nguyen ham • Thuc hien f \ 5' Hoat dong cua HS Hoat dgng cua GV Ggi y tra loi cau hoi Cau hoi Tim mot ham sd F(x) ma F(x) = 3x2 GV ggi mot vai HS tra Idi Bai toan cd nhieu dap sd Tong quat : F(x) = x^ + C C la hang sd bat ki Cau hoi Ggi y tra Idi cau hoi Tim mot ham sd F(x) ma FYY^ — Lam tuong tu cau a F(x) = r vx; — cos X In X - ^ cos X • GV neu dinh nghia : Cho hdm sof(x) xdc dinh tren K Ham soF(x) duac ggi Id nguyen hdm cda hdm sof(x) tren K neu F '(x) - f(x) vai mgi x e K • GV neu va thuc hien vf du 1, GV cd the lay mdt vai vi du khac HI Tim nguyen ham ciia ham sd y = x H2 Tim nguyen ham cua ham sd y = x H3 Tim nguyen ham cua ham sd y = x H4 Tim nguyen ham ciia ham sd y = x" • Thuc Men f\2 5' Hoat dong ciia GV Hoat dong ciia HS Cau hoi Ggi y tra loi cau hoi GV ggi mot vai HS tra Idi Bai toan cd nhieu dap sd Tim mot ham sd F(x) ma F(x) = 2x Tong quat : F(x) = x^ + C dd C la hang sd bat ki Cau hoi Ggi y tra loi cau hoi Tim mot ham sd F(x) ma Lam tuong tu cau a V{x)=- F(x) = hix + C X H5 Tim nguyen ham ciia ham sd y = sin x H6 Tim nguyen ham cua ham sd y = cosx H7 Tim nguyen ham ciia ham sd y 2Vx N/2 H8 Tim nguyen ham ciia ham sd y = x • GV neu dinh li 1: Neu F(x) Id mot nguyen hdm cua hdm sof(x) tren K thi vai moi hang so C, hdm soG(x) = F(x) + C cUng Id mot nguyen hdm cda f(x) tren K H9 Biet ham sd cd mdt nguyen ham la y = sin x Hay tim nguyen ham cua ham sd dd HIO Biet ham sd cd mdt nguyen ham la y = cosx Hay tim nguyen ham cua ham sd dd H l l Biet ham sd cd mdt nguyen ham la y = ^^ '^ Hay tim nguyen ham cua ham sd dd H12 Biet ham sd cd mdt nguyen ham la y = ^ Hay tim nguyen ham ciia ham sd dd • Thuc hien Sgr 5' Hoat dgng ciia GV Cau hdi Hoat dgng ciia HS Ggi y tra loi cay hoi II CHUAN BI CUA GV VA HS Chuan hi ciia GV • Chudn bi cac cau hdi ggi md • Chuan bi mdt bai kiem tra • Chudn bi pha'n mau, va mdt so dd dung khac Chuan bi cua HS Can dn lai mdt so kien thiic da hgc ve nguyen ham va tich phan Lam bai kiem tra tiet HI PHAN PHOI T H d l LUONG Bai chia lam tiet: Tii't : On tap Tii't : Kiem tra IV TIEN TRINH DAY HOC HOAT DONG ON TAP GV dua cac cau hdi sau day Cdu hdi Neu dinh nghia va tinh chat cua : - Nguyen ham - Tfch phan - Neu mdi quan he giiia nguyen ham va tfch phan Cdu hoi Neu cac phuong phap tfnh nguyen ham va tfch phan Cdu hoi Neu cac budc tim nguyen ham bdng phuong phap ddi bien so 62 Cdu hdi Neu cac budc tim nguyen ham bdn-g phUOng phap nguyen ham timg phdn Cdu hdi Neu cac budc tinh tich phan bdng phuong phap doi bien sd Cdu hdi Neu cac budc tfnh tfch phan bang phuong phap tfch phan timg phdn Cdu hdi Neu cdng thiic tfnh dien tich hinh phdng Cdu hdi Neu cdng thiic tinh the tich mdt hinh khdng gian Cdu hdi Neu cdng thiic tfnh the tich mdt hinh trdn xoay bdt ki khdng gian HOAT DONG \iae^ -\) cau d vl + sin2x = |sinX + cosx| = \'2 sin(x + —) 71 Sii dung phuang phap ddi bien so: dat x + — = t Ddp sd 2V2 Bai Hudng ddn Dua vao tinh chat ciia tich phan va cac phuong phap tinh tich phan ^ n •2 ^ ('l-cos2x^ cos2x cau a cos2x.sin X = cos2x = V ; cos4x : 4 65 Ddp sd n cau b Pha bd dau gia tri tuyet ddi bang each them can trung gian 1= r(2'^_±|dx+ |l2^- —Vx Jl 2M , Ddp sd A 2^ J In cau c Phan tich tii so da thiic Ddpsd cau d ^ + llln2 z 1 x'-2x-3 x-3 x+1 Ddp sd - — In cau e / = j(l + sin2x)Jx Tt Ddp so + ^ z cau g ^= j x^+2xsinx + „, , Tl l-cos2x dx 5TI Dap so - - + - ^ Bai Hudng ddn Dua vao cong thiic tinh dien tich hinh phang va the tich hinh trdn xoay Cau a GV cho HS ve hinh 66 HI Tfnh cac can cua tfch phan H2 Tfnh dien tfch : S = 2j|Vr^-(l-x)]dx caub V = 47rJ|Vl-x2-(l-x)j dx HOAT DONG OfiP ^N B6i T6P TR^C NGHIEM (C) (D) (B) (C) a) (C) b) (B) 6.(D) MOT SO DE KIEM TRA THAM KHAO Del Phdn I Trac nghiem khdch quan (4 diem) Cdu Hay dien diing, sai vao d trdng sau day : n xdx = X + C (a) (b) j xdx = C D (c) fxdx = x^+C D (d) fxdx = - x + C D Cdu Hay dien diing, sai vao d trdng sau day : D- (a) ff (x)dx = 1 D (b) ff (x)dx = 1 b a (c) ff(x)dx= ff(x)dx a b b a (d) ff(x)dx = - ff(x)dx a D D b Cdu Ix dx bdng: (a) \ 68 ^\: (c) cd nghiem — ; , | Cdu Cho dudng cong f(x) = x^ Dien tich hinh phdng gidi han bdi f(x) = x true tung, true hoanh va x = la (a)f; (b)2; (e) cd nghiem - ; (d) - Phdn Tu ludn (6 diem) Tinh cac tfch phan sau: ;r a) (x sinxdx; / ^ b) f-^; dx 3^x^-3x + 2 Tinh dien tich hinh phang gidi han bdi f (x) = Vx^ - , y = 2x va true hoanh Di2 Phdn I Trac nghiem khdch quan (4 diem) Cdu I Hay dien diing, sai vao d trdng sau day (a) Mgi ham so deu cd nguyen ham [j (b) Ham sd lien tuc tren (a ; b) thi cd tich phan tren [a ; b] [j (c) jsinxdx = COS2-COS LJ (d) jsinxdx = cos 1-cos2 [J Tt Cdu jx cos xdx bang (a) ; (b)-2; (c) Tt (d)-7i 69 71 Cdu X sin xdx bdng (a) ; (b) -2; (C) Tt ( d ) -71, (c) ^e2 (d) e^ e Cdu X In xdx bdng (a)-e2; (b)-e?; O Phdn Tu ludn (6 diem) Tinh cac tich phan sau : TT h) Jsin3xcos5xdx a) fx(l-x)^°°^dx ; Cho ham so y = f(x) lien tuc tren doan [a ; b] b D ai)) Chiing ~ ' ^ minh • " rang ~ ^ : b D f(x)dx = f(a + b-x)dx a a 71 b)Tinh ln(l + tanx)dx Di3 Phdn Trac nghiem khdch quan (4 diem) Cdu Hay dien diing, sai vao d trdng sau day : 70 (a) f(x + l)dx = - x + x + C • (b) f(3x + l)dx = - x + x + C • (c) f2xdx = x2+C U (d) fxdx = x^+C n Cdu Hay dien diing, sai vao d trdng sau day : (a) J(x200«-x + l)dx = D 1 (b) f(x20°«-x + l)dx = l D (c) f x ( l - x ) d x - D b a (d) ff (x)dx - - ff (x)dx a D b Cdu3 \lx^-l\dx bang: (0 I 11 D 12 D (c) Jf(x)dx = ^ D (b) jf(x)dx 1 D (d) rf(x)dx = l Trd Idi (a) (b) D S (c) (d) S S Cdu Cho ham sd y = 1 (a) Khong ton tai f(x)dx D (b) ff(x)dx... hang sd thi b mib - a) < f/•(x)dx < M(6 - a) 45 §3 Ifng dung cua tich phan hinh hoc (tiet 11 , 12 , 13 , 14 ) I MUC TifeU Kien thirc HS nam dugc : Khai niem dugc ling dung hinh hgc nhu the'' nao? 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