TUYN TP THI I HC CAO NG 1 x-x ũ (2x - 1)e dx (H Dc_81 ) a cos x bcos x ộ pự Vi x ẻ ờ0; ỳ xỏc nh a,b cho = + cos x - sin x + sin x 4ỷ p/ dx dx Tớnh I = ũ (H BK TH_82) J= cos x cos x p/ ũ ũ (3x + 1)dx (B ) (B ) (x + 3)3 sin x - cos x + dx sin x + 2cos x + xdx ũ (x + 1)3 (B ) x -1 ũ x + dx p ũe 2x p/ ũ 10 cos xdx + cos 2x (B ) -1 x - 2x cos a + ,(0 (H AN_96) x sin xdx ũ + cos2 x (HV KTQS_99) dx 99 ũ (HV KTQS_97) (HV KTQS_98) cos x ln(1 + cos x)dx 1/ x cos x (HV KTQS_96) sin x -11 + x + p/ 98 dx sin x - sin x ũ dx (HV KTQS_95) 4sin x p/3 KT (HV KT Mt Mó_00) ũ (x + 1)2 p/4 (HV QY_98) (HV p/3 x +1 94 dx (HV QY_99) -p / 4 (H AN_97) Mt Mó_99) p/ ũ 102 ũ xe 2x p 103 sin xdx (H AN_99) x x +9 p ũ 3sin 2 x x + 1dx dx (PV BC TT_98) ln + ln x 106 ũ dx x p/ ũ 107 + sin 2x cos x 108 ũ (1 + x) ũ 111 (H Lut _00) 2x (H C_98) e dx dx x e +1 dx ũ e2x + p/ 112 (PV BC TT_00) dx ũ + x3 110 (PV BC TT_98) 3dx 109 p/ ũ ũ p/ ũ cos xdx + cos x p/ dx + sin 2x ln(x + 1) x + sin 2x + cos 2x ũ sin x + cos x dx p/6 113 (H TD TT_00) ũ (x ln x) e ũ xdx 105 dx ũ 104 (H AN_98) ũx dx dx ũ cos4 x (cos x + sin x)dx p/2 ũ ũ (2x - 1)cos xdx (H C_00) dx ũ (H C_99) (1 + e x ) + e2x e2x sin 3xdx dx (H NN I_97) (H NN I_98B) 114 ũ x(1 - x)19 dx (H NN I_99B) 115 p/ dx ũ x(x + 1) ũ p/2 116 xtg 2xdx (H NN I_00) cos x dx p / sin x ũ (H NN I_01A) 117 ũ ln(1 + x)dx 1 118 ũ x + sin x -1 p/ ũ 119 x2 + (H Lõm Nghip_97) dx (H Lõm Nghip_98) dx + sin x + cos x (H Lõm Nghip_00) 120 ũ x sin xdx (H SP HN I_99D) a 121 ũ x a - x dx (a > 0) (H SP HN I_00) 122 ũ x3 - x dx (H SP HN I_01B) 123 ũ xdx (H THp_93) -1 x + p 124 ũ x sin xdx p/ ũ 125 ũ (H QG_96) x sin xdx ũ + cos x x dx ũ - x2 dx sin x + cos x dx ũ1+ p/ 126 (H THp_94) xdx ũ - x2 dx x +1 + x (H QG_97A, B, D) 127 dx ũ ex + ũx p/ ũ + x dx 0 p/6 sin x cos x dx (H QG_98) p/6 sin x cos2 x dx; J = ũ dx 128 Tớnh I = ũ sin x + cosx sin x + cos x 5p / cos2x T ú suy ra: ũ (H QG HCM_01A) dx p / cosx - sin x p/ ũ 129 p/4 5e x sin 2xdx ũ 0 2cos xdx + 2sin x (H SP II _97) 130 Cho f(x) liờn tc trờn R : f (x) + f ( - x) = - 2cos 2x "x ẻ R Tớnh 3p / ũ f (x)dx (H SP II _98A) ũ (sin10 x + sin10 x - cos x sin x)dx (H SP II _00) -3p / p/ 131 132 ũ 3x + x2 + 1 ũ dx -1 p/4 133 ũ x - x dx ũ p dx x+4+ x+2 (C SP HN_00) (sin x + 2cos x) dx 3sin x + cos x (C SP HN_00) 134 ũ sin x cos xdx p/ 135 ũ 136 ũ -1 137 dx ũ x(1 + 1 ũ - x arcsin xdx -1 t3 ũ t + 2t + dt 139 + sin x ln( )dx + cos x x x ũ (e sin x + e x )dx -1 138 (C SP MGTW_00 ) ũ + x2 1/ + x - x2 + 2x dx (C PCCC_00) (H TN_00) (H SP Vinh_98) dx (C SP KT_00) x) ũ x + 1dx (H SP Vinh_99) 140 ũ (x + x)dx x +1 p ũ sin 141 (H H_99) p/4 ũ x cos3xdx 142 ũ ln x x2 p/ ũ 143 144 sin x p/ dxS (H Hu_00) p/ p + cos x dx p/ ũ (H N_97) cos x ũ 146 (H Hu_98) dx + x +1 ũ 145 (H H_00) dx sin x + cos x dx + tgx cos xdx ũ + sin x dx (H N_98) ũ x ln xdx cos x p/2 sin x - cos x 147 ũ dx sin x + cos x p/ ũ (H N_99) sin xdx + 2cos x (H N_00) 148 ũ x + x + arctgx dx + x2 x +1 149 ũ dx 3x + e 150 ũ 2 + ln x dx 2x ũ (1 + 3x)(1 + 2x + 3x ũ e p cos3 x dx sin x + cos x ln xdx ũ x(ln x + 1) 10 ) dx (H Quy Nhn) 151 ũ x x3 + 1dx p/ (H Tnguyờn_00) ũ e ũ sin xdx 1 ln x dx x ũ x2 + dx x +1 ũ sin3 x dx sin x + cos x p/ 2 x ũ x e dx (H Lt) (H Cn p/ ũ sin x + cos x x ũ1+ sin 4x x dx dx Th) p/ ũ 152 ũ p/ sin xdx cos x + p/2 ũ dx p ũx ũ + 3x ũx xdx ũ 157 ũ p/ ũ e- x x ũ - x dx x -1 ũ x sin xdx p/ ũ dx sin 2x x dx ũ sin x cos xdx ũ cos p (H SP HCM) p 4x + 11 ũ x + 5x + dx + cos p/ 2 (H Ngoi thng) ũ arctg(cos x)dx sin xdx sin x + cos x - sin xdx p x sin xdx ũ + e- x dx 1/ (H Y Dc HCM) ũ + cos x p/ BK -p 1 156 p sin xdx ũ x ln p - xdx -p e (H xdx x sin x ũ 155 x cos xdx ũ (2x + 1)3 ũ + 4cos x dx p (H Thu sn NT) dx x +1 cos 2xdx ũ x + 2x3 ũ (x + 1)sin xdx 153 sin x cos x(1 + cos x)2 dx 0 p/ 154 ũ sin 2x(1 + sin x) dx p/ ũ p/ xdx p ũx sin xdx sin 2xdx + sin x xdx 2x + 1 ũe x p/4 ũ sin xdx sin ( px)dx (H QG HCM) HCM) 1 ộ xự e 158 ũ ỳỷ dx + x ũ (x - 1)e ũ x - dx 159 ũ x(x - 4) ln 2 + ln x dx x 160 ũ x + 2x 161 162 ũ e e 2x 2x 20 + 3e ũ dx (1 + e x ) x4 ũ x +1 ex dx + 3e x + dx dx (C SP_04A) (C GTVT_04) (C KTKT_04A) dx BI TP V DIN TCH HèNH PHNG Tớnh din tớch hỡnh phng gii hn bi cỏc ng { } 1, 54 : S = x + y = 0; x - x + y = { 2, 95 : S = y = x; y = sin x + x; x = 0; x = p { 3, 96 : S = y = x; + y = ( x - 1) } } 4, 99 : Parabol y = x chia ng trũn (O; R = 2) theo t s no ỡ 5, 134 : S = f ( x) = ợ Hc) (DL) x ũ ( x+2 - x-2) -3 Tin x2 + NN 0 ũ (HDL dx - x dx e x ũe ũ dx 2x ỹ x2 ; y = 0; x = 1ý 8x +1 ỵ 6, Bỏch Khoa 93 : Tỡm b cho din tớch hỡnh phng gii hn bi cỏc ng sau bng ỡ x2 pỹ S = y = ; y = 1; x = 0; x = ý x +1 2ỵ ợ p ỡ ợ 7, Bỏch Khoa 2000 : S = y = sin x.cos3 x; y = 0; x = 0; x = { pỹ ý 2ỵ } 8, Kin Trỳc 94 : S = y = x - x + ; y = - x { 9, M Thut CN 98 : S = y = x ; y = x } ỡ 27 ỹ x2 10, M a Cht 98 : S = y = x ; y = ;y= ý xỵ 27 ợ ỡ 11, Bu Chớnh VT 98 : S = y = ợ - x 8x 7- xỹ + - ;y= ý 3 x -3ỵ ỡ 12, Bu Chớnh VT 2000 : S = y = - 2sin ợ 3x 12 x pỹ ; y = 1+ ;x = ý p 2ỵ { } 13, HVNH TPHCM 99 : S = y = x x + 1; y = 0; x = 0; x = { } 14, Kinh T QD 94 : S = y = xe x ; y = 0; x = 0; x = { 15, Thng Mi 96 : S = y = x ; x = - y } { } 16, Ti Chớnh K Toỏn 2000 : S = y = e x ; y = e - x ; x = 17, M 2000 : S = { y = sin x ; y = x - p } 18, Quõn Y 97 : Tớnh din tớch hỡnh phng gii hn bi cỏc ng y = ; y = x3 - x + x - v tip tuyn vi ng cong ti x = ỡ ợ 19, HVKT Quõn S 2000 : S = y = 1 p pỹ ;y= ;x = ;x = ý 2 sin x cos x 3ỵ ỡ ợ 20, Cụng on 98 : S = y = ( + cos x ) sin x; y = 0; x = ỡ x2 21, Cụng on 99 : S = y = x ; y = ;y= ợ { 22; Cụng on 2000 : S = x = 8ỹ ý xỵ } y ; x + y - = 0; y = p 3p ỹ ;x = ý 2 ỵ ỡ ợ 23, Nụng Nghip I 95 : S = y = ln k ( k > ) ; y = 0; x = 1; x = ỹý x ỵ { } 24, Nụng Nghip I 98B : S = y = x3 - x + x + 6; y = ỡ 25, Nụng Nghip I 99A S = y = ợ x2 ỹ ; y = ý x2 + 2ỵ p pỹ ỡ S = y = tg x; y = 0; x = - ; x = ý 4ỵ ợ { } 26, Nụng Nghip I 99B : S = y = x - 3x + 2; y = 0; x = 0; x = { } 27, Nụng Nghip I 2000A : S = y = 0; x - y + = 0; x + y - = { } { } 28, S Phm I 2000A : S = y = x - ; y = x + 29, S Phm I 2000B : S = y = x - x + ; y = ỡ ợ 30 , Quc Gia 93 : S = y = ln x ; y = 0; x = { 31, Quc gia 97A : S = y = x3 ; y = - x ỹ ; x = 10 ý 10 ỵ } ỡ 32, DL Phng ụng 2000: S = x = 1; y = 0; y = ợ { ỡù ỹù ỹ ; S = x = 1; x = 2; y = 0; y = ý ý x (1 + x3 ) ỵù x2 - x6 ỵ ùợ x2 } 33, C Kim Sỏt 2000 : S = y = ( x + 1) ; y = 0; x = sin p y;0 Ê y Ê { } 34, Bỏch Khoa 2001A : S = y = - - x ; x + y = { } 35, HVCNBCVT 2001 : S = y = x.e x ; y = 0; x = -1; x = ổ5 ố2 ứ 36, Kinh T QD 2001 : (P) : y = x - x v hai tip tuyn qua M ỗ ;6 ữ ỡ 37, Cụng on 2001 : S = y = ợ ỹ x + 2ax + 3a a - ax ; y = ( a > )ý Tỡm giỏ tr MAX ca din tớch ú 4 a +1 a +1 ỵ { } 38, Y Thỏi Bỡnh 2001 : S = y = x - ; y = 0; x = 0; y = - x ỡ 39, Cnh Sỏt Nhõn Dõn 2001 : S = x = 0; x = ợ ỹ x ;y = ; y = 0ý - x4 ỵ { } 40, Khi A 2002 : S = y = x - x + ; y = x + ỡù x2 x ỹù 41, Khi B 2002 : S = y = - ; y = ý x ùỵ ợù ỡ ợ 42, Khi D 2002 : S = y = -3 x - ỹ ; x = 0; y = ý x -1 ỵ { )} ( 43, Khi A 2007 : S = y = ( e + 1) x; y = + e x x BI TP TRấN BO TON Bi Tớnh cỏc tớch phõn : a) I = p tan x ũp cos x + cos x dx ; b) J = x3 ũ0 (1 + x )3 dx ; c) I = ũ0 -3x + x + dx ; dx c) I = ũ ; x 1+ x g) I p sin x d) J = ũ dx ; + cos x x (2 cos2 x.cos x).esin x dx ; e) x3 x dx x3 ex x h) I= x( tan x).dx cos x x Bi Tớnh dt hỡnh phng gii hn bi cỏc ng y2 = x3 v y2 = ( x )3 (s : S =8/5 ) II CC THI TT NGHIP Tớnh cỏc tớch phõn sau: TN, 1994 (2 im) ; 1) S: 1) 2) ; 15 2) - e3 TN, 1996 (2 im) 1) S: 1) 2) 248 35 ln - ; 2) - 2 TN, 1997, t (2 im) S: 1) 2) 1) 18ln3 - 8ln2 - ; 2) 16 + 15 TN, 1997, t 1) S: ln - TN, 1998, chớnh thc (2 im) S 1) 2) 1) - 2; 2) TN, 1998, t (2 im) 1) S: e - +p e TN, 1998, t (2 im) 1) S: 39 - 12 ln S: p TN, 1999, t (2 im) ; TN, 1999, t (2 im) 1) Tớnh tớch phõn (S: 2) Gii phng trỡnh TN, 2000 1) Cho hm s ) 15 Hóy tớnh o hm v gii phng trỡnh ; 2) Cú tem th khỏc v bỡ th cng khỏc Ngi ta mun chn t ú tem th, bỡ th v dỏn tem th y lờn bỡ th ó chn Mi bỡ th ch dỏn mt tem th Hi cú bao nhiờu cỏch lm nh vy TN, 2000 - 2001 (1 im) 1) Tớnh tớch phõn (S: 3 - p ) 32 TN, 2001 - 2002 (2 im) 1) Tỡm giỏ tr nh nht v giỏ tr ln nht ca hm s F(x) = cos2x + 4sinx ộ pự trờn on 0; ỳ 2ỷ 2) Cú bao nhiờu s t nhiờn chn cú bn ch s ụi mt khỏc nhau? TN, 2002 - 2003 (2 im) 1) Tỡm nguyờn hm Bit rng ca hm ca hm s 2) Tớnh din tớch hỡnh phng gii hn bi th hm s v ng thng ỏp s 1) 2) (TN 2003 2004) Tớnh th tớch ca vt th trũn xoay hỡnh phng gii hn ca th hm s cỏc ng quay quanh trc (TN, 2005) v S .S: TN khụng phõn ban, 2006) Tớnh din tớch hỡnh phng gii hn bi cỏc th hm s v ng thng Tớnh tớch phõn ỏp s 1) (TN 2006, Ban KHTN) S (TN 2006, Ban KHXH) S (TN khụng phõn ban, 2007) S (TN ban KHTN, ln 1, 2007) S (TN ban KHXH, ln 1, 2007) S (TN khụng phõn ban, 2007) S (TN ban KHTN, ln 2, 2007) Cho hỡnh 2) gii hn bi cỏc ng Tớnh th tớch trũn xoay c to thnh quay hỡnh quanh trc honh S (TN ban KHTN, ln 2, 2007) Tớnh din tớch hỡnh phng gii hn bi cỏc ng (.v.d.t.) v S 36 [...]... Tớnh din tớch hỡnh phng gii hn bi cỏc ng y = 0 ; y = x3 - 2 x 2 + 4 x - 3 v tip tuyn vi ng cong ti x = 2 ỡ ợ 19, HVKT Quõn S 2000 : S = ớ y = 1 1 p pỹ ;y= ;x = ;x = ý 2 2 sin x cos x 6 3ỵ ỡ ợ 20, Cụng on 98 : S = ớ y = ( 2 + cos x ) sin x; y = 0; x = ỡ x2 2 21, Cụng on 99 : S = ớ y = x ; y = ;y= 8 ợ { 22; Cụng on 2000 : S = x = 8ỹ ý xỵ } y ; x + y - 2 = 0; y = 0 p 3p ỹ ;x = ý 2 2 ỵ ỡ ợ 23, Nụng Nghip... Bỏch Khoa 2001A : S = y = - 4 - x 2 ; x 2 + 3 y = 0 { } 35, HVCNBCVT 2001 : S = y = x.e x ; y = 0; x = -1; x = 2 ổ5 ố2 ử ứ 36, Kinh T QD 2001 : (P) : y = 4 x - x 2 v hai tip tuyn qua M ỗ ;6 ữ ỡ 37, Cụng on 2001 : S = ớ y = ợ ỹ x 2 + 2ax + 3a 2 a 2 - ax ; y = ( a > 0 )ý Tỡm giỏ tr MAX ca din tớch ú 4 4 a +1 a +1 ỵ { } 38, Y Thỏi Bỡnh 2001 : S = y = 5 x - 2 ; y = 0; x = 0; y = 3 - x ỡ 39, Cnh Sỏt Nhõn Dõn... x2 x 2 ỹù 41, Khi B 2002 : S = ớ y = 4 - ; y = ý x 4 2 ùỵ ợù ỡ ợ 42, Khi D 2002 : S = ớ y = -3 x - 1 ỹ ; x = 0; y = 0 ý x -1 ỵ { )} ( 43, Khi A 2007 : S = y = ( e + 1) x; y = 1 + e x x BI TP TRấN BO TON Bi 1 Tớnh cỏc tớch phõn : a) I = p 3 1 tan x ũp cos x 1 + cos 2 x dx ; b) J = x3 ũ0 (1 + x 2 )3 dx ; 1 c) I = ũ0 1 3 -3x 2 + 6 x + 1 dx ; 4 2 dx c) I = ũ ; 3 1 x 1+ x 2 g) I 0 p 2 sin 2 x d) J =... x (2 cos2 x.cos x).esin x dx ; 2 e) 1 3 x3 x dx x3 1 ex x h) I= 2 x( 2 2 tan x).dx cos x 3 x 4 Bi 2 Tớnh dt hỡnh phng gii hn bi cỏc ng y2 = x3 v y2 = ( 2 x )3 (s : S =8/5 ) II CC THI TT NGHIP Tớnh cỏc tớch phõn sau: TN, 1994 (2 im) ; 1) S: 1) 2) 8 ; 15 2) 8 - 2 e3 9 TN, 1996 (2 im) 1) S: 1) 2) 248 35 ln 2 - ; 3 2 2) 2 - 2 2 3 TN, 1997, t 1 (2 im) S: 1) 2) 1) 18ln3 - 8ln2 -... dỏn mt tem th Hi cú bao nhiờu cỏch lm nh vy TN, 2000 - 2001 (1 im) 1) Tớnh tớch phõn (S: 3 3 - p ) 32 TN, 2001 - 2002 (2 im) 1) Tỡm giỏ tr nh nht v giỏ tr ln nht ca hm s F(x) = 2 cos2x + 4sinx ộ pự trờn on ờ 0; ỳ ở 2ỷ 2) Cú bao nhiờu s t nhiờn chn cú bn ch s ụi mt khỏc nhau? TN, 2002 - 2003 (2 im) 1) Tỡm nguyờn hm Bit rng ca hm ca hm s 2) Tớnh din tớch hỡnh phng gii hn bi th hm s v ng thng ỏp s 1) 2)... (TN ban KHTN, ln 1, 2007) S (TN ban KHXH, ln 1, 2007) S (TN khụng phõn ban, 2007) S (TN ban KHTN, ln 2, 2007) Cho hỡnh 2) gii hn bi cỏc ng Tớnh th tớch khi trũn xoay c to thnh khi quay hỡnh quanh trc honh S (TN ban KHTN, ln 2, 2007) Tớnh din tớch hỡnh phng gii hn bi cỏc ng (.v.d.t.) v S 36 ... tip tuyn vi ng cong ti x = ỡ ợ 19, HVKT Quõn S 2000 : S = y = 1 p pỹ ;y= ;x = ;x = ý 2 sin x cos x 3ỵ ỡ ợ 20, Cụng on 98 : S = y = ( + cos x ) sin x; y = 0; x = ỡ x2 21, Cụng on 99 : S = y =... : S = y = ( + cos x ) sin x; y = 0; x = ỡ x2 21, Cụng on 99 : S = y = x ; y = ;y= ợ { 22; Cụng on 2000 : S = x = 8ỹ ý xỵ } y ; x + y - = 0; y = p 3p ỹ ;x = ý 2 ỵ ỡ ợ 23, Nụng Nghip I 95 : S =... x = -1; x = ổ5 ố2 ứ 36, Kinh T QD 2001 : (P) : y = x - x v hai tip tuyn qua M ỗ ;6 ữ ỡ 37, Cụng on 2001 : S = y = ợ ỹ x + 2ax + 3a a - ax ; y = ( a > )ý Tỡm giỏ tr MAX ca din tớch ú 4 a +1 a +1