Thiết kế bài giảng giải tích lớp 12 tập 2

w Ss^ TRAN VINH I hiet ke bai giang GIAI TICH ]2 TAP HAI f-'.i mmT: /-, ^* ' r >' »3c I'tl'l ^ NHA XUAT BAN HA N6I 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 1 NHJtXG VAX DE CUA CHMfONG I. NOI DUNG Noi dung chinh cua chucung 3 : 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 1. Kien thiirc Nam dugc toan bo kien thiic co ban trong 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 trong hinh hoc : Tinh dugc dien tich hinh phang, the tich vat the trong khong gian. 2. KT nang van dung cac nguyen ham co ban de tinh cac nguyen ham. Van dung thanh 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. 3. Thai do Tu giac. tich cue, dgc lap va chii dgng phat hien ciing nhu ITnh hoi kien" thiic trong qua trinh hoat dgng. Cam nhan dugc su cSn thiet cua dao ham trong viec khao sat ham so. Cam nhan dugc thuc te cua toan hgc, nhat la doi vdi dao ham. PHan 2. CAC BAI SOA]!!^ §1. Nguyen ham (tiet 1, 2, 3, 4, 5) I. MUC TIEU 1. 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. 2. KT nang HS tinh thanh thao cac nguyen ham co ban. Tinh dugc nguyen ham dua vao phuong phap doi bien sd va phuong phap nguyen ham tiing phan. 3. Thai do Tu giac, tich cue trong hgc tap. Biet phan biet ro cac khai niem co ban va van dung trong tiing trudng hgp cu the. " Tu duy cac va'n de cua toan hgc mot each Idgic va he thdng. n. CHUAN BI CUA GV VA HS 1. Chuan bj ciia GV Chuan bi cac cau hoi ggi mo. Chuan bi pha'n mau, va mdt sd dd diing khac. 2. Chuan bj cua HS Can dn lai mot sd kien thiic da hgc ve dao ham. ra. PHAN PHOI THCJI LUONG Bai nay chia lam 5 tiet: Tiet 1 : Tic dau den hit miic 2 phdn I. Tiet 2 : Tiep theo den het phdn I. Tiet 3 : Tiep theo den het muc I phdn II. Tiet 4 : Tiep theo den het phdn II. Tiet 5 : Bdi tap IV TIEN TRINH DAY HOC A. DAT VAN OE Cau hoi 1 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 2 Chohamsdy= 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 HAM VA TINH CHAT HOATDONC1 1. Nguyen ham • Thuc hien f\ 1 trong 5' Hoat dgng cua GV Cau hoi 1 Tim mot ham sd F(x) F(x) = 3x2 Cau hoi 2 Tim mot ham sd F(x) FYY^ — r vx; — cos X ma ma Hoat dong cua HS Ggi y tra loi cau hoi 1 GV ggi mot vai HS tra Idi. Bai toan nay cd nhieu dap sd. Tong quat : F(x) = x^ + C trong do C la hang sd bat ki. Ggi y tra Idi cau hoi 2 Lam tuong tu cau a. In X F(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" 4 • Thuc Men f\2 trong 5'. Hoat dong ciia GV Cau hoi 1 Tim mot ham sd F(x) ma F(x) = 2x. Cau hoi 2 Tim mot ham sd F(x) ma V{x)= X Hoat dong ciia HS Ggi y tra loi cau hoi 1 GV ggi mot vai HS tra Idi. Bai toan nay cd nhieu dap sd. Tong quat : F(x) = x^ +C trong dd C la hang sd bat ki. Ggi y tra loi cau hoi 2 Lam tuong tu cau a. F(x) = hix + C. H5. Tim nguyen ham ciia ham sd y = sin x. H6. Tim nguyen ham cua ham sd y = cosx. 1 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. 1 Hll. 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 3 trong 5'. Hoat dgng ciia GV Cau hdi 1 Hoat dgng ciia HS Ggi y tra loi cay hoi 1 [...]... l 2x (a)y=x' +2 ; (b)y=2x; (c) y = 2 ; (d)y= VST Trd led (c) 18 Cdu 5 Ham sd nao sau day cd nguyen ham la Vx (a)y= y = ^ ^ ; 2Vx (b) y = - x 2 ; 3 (c)y = x2; (d)y=- X Trd Idi (a) Cdu 6 Ham sd nao sau day cd nguyen ham la - cos 2x (a) y = sin2x ; (b) y = —sin2x; (c) y = -sin2x; (d)y=cos2x Trd Idi (b) Cdu 7 Ham sd nao sau day cd nguyen ham la cos 2x (a) y = sin2x ; (b) y = — s i n 2 x ; (c)y = -sin2x;... {2x + lf Cau hdi 2 Tfnh tfch phan da cho Hoat dgng cua HS Ggi y tra Idi cau hdi 1 {2x + lf=4x^+4x + \ Ggi y tra Idi cau hdi 2 1 1 13 I = f(2x +1)^ dx = f(4x^ + 4x + l)dx = ' 3" 0 0 Cau 2 Hoat dgng ciia GV Cau hdi 1 Dat u = 2x + 1, tfnh du Hoat dgng ciia HS Ggi y tra Idi cau hdi 1 Ta cd du = 2dx 31 Cau hdi 2 Ggi y tra loi cau hdi 2 Bien doi I theo bien u Dat u = 2x + 1, ta cd uiO) = 1, u(l) = 3 va (2x... a 2 sin X la mdt nguyen ham ciia sin2x c) Lam tuong tu cau a 4^ e^ la mdt nguyen ham cua 1 X) Bai 2 Hudng ddn Su dung cac tinh chat ciia nguyen ham cau a Chia tii cho miu, sau dd sii dung tinh chat ciia nguyen ham ciia ham sd y = x" 5 7 2 Ddp sd — x3 +—x^ +7;X^ + C 5 7 2 2' ' + In 2 - 1 cau b Ddp so + C e''an2-l) cau c Su dung cong thiic lugng giac va nguyen ham ciia ham sd lugng giac Ddp sd -2cot2x... tra loi cau hdi 3 Sit)=^^^y\t ts[l- l) = t' + t 2, 5] cau 3) Hoat dgng cua G V Hoat dgng ciia HS Ggi y tra loi cau hdi 1 Cau hdi 1 Chiing minh S(t) la nguyen Vi S'it) = 2t+l,t e[l ; 5], nen Sit) ham cua f(t) = 2x + 1 la mdt nguyen ham ciia fit) = 2t + I Cau hdi 2 24 Ggi y tra loi cau hdi 2 Chirng minh S = S(5) - S(l) cJ = S ( 5 ) - 5 ( l ) = 2 8 - 0 = 28 • Tiep theo GV sii dung hinh 47 de' mo ta dien... la hdm sd dudi dd'u tich phdn 26 a H2 Chiing minh Jf (x)dx = 0 a b a H3 Chiing minh ff (x)dx = - jf (x) a b • GV neu chii y trong SGK • Thuc hien vf du 2 trong 5' GV cd the la'y vf du khac cau a Hoat dgng cua GV Cau hdi 1 Hoat dgng cua HS Ggi y tra Idi cau hdi 1 Tim nguyen ham F(x) ciia F(x)= f2xdx = x^ ham sd y = 2x Ggi y tra Idi cau hdi 2 Cau hdi 2 HS tu tfnh 2 Tfnh J2xdx 1 caub Hoat dgng cua GV Hoat... 2 [\fix)Ax+ +[\gix)dx] H 22 Tinh [(cos x + tan x)dx H23 Tinh [(cosx - vx)dx H24.Tinh |(x^+x + l)dx 10 + gix) Ggi y tra loi cau hoi 2 [lfix)dx - jgix)dx] = fix) - gix) • GV neu va thuc hien vi du 4 GV cd the thay bdi vi du khac H21 Tinh J (cos x + sin x)dx ^fix) nOATiyDNG3 3 Sii ton tai nguyen ham • GV n6u dinh li 3: Moi hdm sof(x) lien tuc tren K deu co nguyen hdm tren K • Thuc hidn vi du 5: 2 H25... sau day cd nguyen ham la cos 2x (a) y = sin2x ; (b) y = — s i n 2 x ; (c)y = -sin2x; Trd Idi (b) (d)y=sin2x Cdu 8 Ham so nao sau day cd nguyen ham la sin2x (a) y = sin2x ; (b) y = —cos2x; 2 (d)y=sin2x (c) y = -sin2x; Trd Idi (b) Cdu 9 Ham so nao sau day cd nguyen ham la e" (a)y = e ' ' ; (b)y=^e2''; (c)y = lnx; (d)y=e'"'' Trd Idi (a) Cdu 10 Ham so nao sau day cd nguyen ham la In x (a)y = l n x ; (b)y=-;... tra loi cau hoi 2 [(x-iyOdx^[u'Odu = - u i ' + C = l(x-i)"+C U caub Hoat dgng ciia GV Hoat dgng cua HS Cau hdi 1 Ggi y tra loi cau hdi 1 Dat x = e' tinh dt Ta cd t = Inx => dt = —dx X Cau hoi 2 Tinh [ Ggi y tra loi cau hdi 2 dx •' X [^^dx=[tdt= ^2^ C=^ln2x + C J 2 2 J X • GV neu dinh li 1: Neil \fiu)du tuc thi = Fiu) + C vdu = u(x) la hdm so co dao hdm lien \fiuix))u 'ix) dx = Fiuix)) + C H27 Hay chiing... 1 1 cos8x + cos2x + C cau e Sir dung cong thiic lugng giac va nguyen ham cua ham sd lugng giac Ddp sd tanx - x + C cau g Dat 3 - 2x = u Ddpsd - - e ^ ' ^ ^ + C 2 20 1 1/ 1 • (1 + x)(l - 2x) ~ 3 1 + X cauh 1 +X Ddp sd — In l-2x + 1 - 2x + C Bai 3 Hudng ddn Su dung cac tinh chat ciia nguyen ham cau a Dat u = 1- x - (1-x) 10 Ddp sd 10 - + C cau b Dat u = 1 + x' 5 Ddpsd - ( l + x ^ ) 2 + c cau c Dat... nguyen ham tirng phan : u = I n ( l + x), dt; = xdx Ddp sd \ix^ - l ) l n ( l + x) - j x ^ + I + C 2 X Cau b u = X + 2x - 1, du = e dx Ddp sd e"" (x^ - 1) + C cau c.u=x,dv - sin(2x + l)dx X 1 Ddp sd -— cos(2x + 1) + — sin(2x + 1) + C cau d Dat u = 1 - X, dy = cosxdx Ddp sd (1 - x) sin x - cos x + C 21 2 Tich phan (tiet 6, 7, 8, 9, lO) I MUC TIEU 1 Kien thiic HS nam dugc ; Khai niem tich phan la gi? . = X - 1, tinh du Cau hoi 2 Tinh |(x-l)'°dx. Hoat dgng ciia HS Ggi y tra loi cau hoi 1 Ta cd du = u'dx = dx. Ggi y tra loi cau hoi 2 12 [(x-iyOdx^[u'Odu = -ui'+C. = fix) - gix). • GV neu va thuc hien vi du 4. GV cd the thay bdi vi du khac. H21. Tinh J (cos x + sin x)dx . H 22. Tinh [(cos x + tan x)dx . H23. Tinh [(cosx - vx)dx . H24.Tinh . hoi 2 Tinh nguyen ham ciia ham sd: 1 Cau hoi 3 Tinh nguyen ham ciia ham so da cho. Hoat dgng ciia HS Ggi y tra loi cau hoi 1 [2x2dx = -x^ J 3 Ggi y tra loi cau hdi 2 1 ^ ' [-^ L=dx-