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LUYỆN THI ĐẠI HỌC TÍCH PHÂN

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TÀI LIỆU THAM KHẢO LUYỆN THI ĐẠI HỌC TOÁN TÍCH PHÂN

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Nội dung Text: LUYỆN THI ĐẠI HỌC TÍCH PHÂN

  1. 21/I = LT ĐH 1 e π 2x 23 81/I = ∫ (ln x)2 dx sin 2 xdx 51/I = ∫ (1 + 2x)(1 + 3x + 3x 111/I = ∫ e ) dx π 0 1 0 2 4 4 ∫ cos 2x(sin x + cos e2 x)dx 1 1 2 2 ln x TÍCH 112/I = ∫ x 2 ln(1 + 82/I = dx )dx 52/I = 1 dx ∫ ∫ 0 x 3 x x 1+ x 1 e π ln x e e2 π 2 22/ I = ln x 113/I = 1 (x + 1)2 dx 3 ∫ PHÂN ∫ cos xdx 83/I = dx ∫ 3 2 2 tg x + cot g x − 2dx 53/I = ln x 0 ∫ 1 e π π 2 1 84/I = ∫ x ln(x 2 + 1)dx 6 2 4sin 3 x 23/ I = dx 1+ x dx 2 114/I = ∫ 1/ 1 1 ∫ ∫ x.ln dx 0 1 + cosx (1 − x 2 )3 dx 54/I = ∫ cos x 1− x 1 3 0 0 dx 85/I = ∫ 13 dx 1 − x 2 dx x2 + 3 24/ I = 2 ∫x 2/ ∫ . 115/I = ∫  ln x  1 1 3 t dx ⇒ I < 2 55*/I = ∫ dx x2 +1  ÷ 0 2x 1 +3 1 x 1 0e dx 86/I = 15 ∫ 3/I= ∫ cos3x.sin 8x dx 1 + x 2 dx 25/I = ∫x 4 − x2 π ex 0 ln 3 0 dx 56/I = 116/I = 3 sin x.ln(cos x)dx ∫ π π2 ∫ x 3 (e + 1) 0 x 1 3 2 0 26/I = ∫ dx 4/I = ∫ 3tg x dx 87/I = 4 2x + 1 sin xdx ∫ π 0 0 π 2x 3 + x + 1)dx 57/I = ∫ x(e 0 4 e2 117/I = 1 1 −1 2 ∫ cos (ln x)dx 27/I = dx π ∫ π x 58/I = 0e +4 1 ln(sin x) 3 4 2 88/I = ∫ (2cotg x + 5) dx dx 5/I = ∫ π π cos 2 x 1 2 π π 28/I = ∫ dx 41 118/I = 26 −x 3 5 dx 6 ∫ 1 − cos x sin x.cos 1 1− e 6 ∫ xdx 0 cos x 2 π 0 e 2x 89/I = ∫ cos(ln x)dx 2 2 1 − cos x π 6/I = 29/I = ∫ dx 1 23 dx 1 ∫ x 1 dx +1 59*/I = 119*/I = 4 0e 0 1 + cos x ∫ dx ∫ 2 x x2 + 4 5 1 + x 2 − x)dx cos3 x 90*/I = ∫ ln( −x 0 π 1e 30/I = dx 0 π ∫ 2 sin2 x.cos2xdx 7/ I = 1 3 x2 −x +1 0e x 120/I = ∫ x e dx ∫ 4 60/I = 1 3 dx ∫ dx 0 91*/I = ∫ 0 0 1 + cos 2x ln x e 2 x −1 dx 31/I = 2 ∫ π π x(ln 2 x + 1) e 2x 1 3 ln 5 (2cos2 x-3sin2 x)dx 8/I = 121/I = 2 esin 2 x .sin x cos3 xdx 83 x +1 61/I = dx ∫ ∫ ∫ 92/I = dx 7 ∫ ex − 1 0 ln 2 0 x x +1 1 32/I = 3 dx π ∫ π π 2 x +1 sin( − x) 3 x3 3x + 1 e 3 0 62/I = ∫ sin 2x 122/I = 2 .ln xdx 93/I = ∫ 2 4 dx dx 9/ I= dx ∫ ∫ 1x x 2 − 16 2 4 π 0 1 + cos 1 x 3 2 −π ∫ (x − 3) x − 6x + 8 dx 33/I = sin( + x) 2 π x 1 4 2 0 3 1 63/I = ∫ dx 123/I = ∫ cos x dx 94/I = 6 + 1) x + 1 π 0 (x 1 1 dx x 2 − 4x − 5 ∫ 0 dx 2 34/I = ∫ 6 − 5sin x + sin x 3 0 (tgx-cotgx)2 dx 10 / I = x2 4 − x2 π ∫ 3 5 2 e2 124/I = ∫ dx π 64/I = 2 sin x.sin 2x.sin 3xdx 1 1 − x 2 − 6x + 9 95*/I = − 1 4 ∫( )dx ∫ 1 6 dx 2 35/I = ∫ ln x e ln x 0 π x 16 − x 2 1 1 2 125/I = dx π ∫ 3 4 11/ I = 4 2 2 65/I = 2 cos 2x(sin 4 x + cos 4 x)dx 96/I = −∫4 x − 4 dx + 8x + 26 ∫ cos x dx −5 2x 1 6 dx ∫ 36*/I = ∫ 0 1 2x + 9 x x2 − 9 0 23 126/I = ∫ x + 3 dx 2 π x 3 − 2x 2 − x + 2 dx 97/I = π ∫ 0 2 12 / I = 22 3 ∫ sin x dx −1 2 37/I = 4 − x dx 23 66*/I = ∫x 3 cos x − sin x )dx 1 4 ∫( 0 3π 127/I = 1 x 2 (x + 1) dx −1 ∫ 0 13*/ I = 4 2 cos 2x + 1dx 98/I = ∫ (x 2 + 4)3 dx x7 38/I = ∫x 3 π sin 2x π 0 67/I = ∫ dx 0 128*/I = −∫π (2 + sin x)2 dx 3 3 sin x − sin x 8 4 21+ x − 2x 2 4 cot gx dx ∫ x2 − 4 4 π sin x π π 2 dx 99/I = ∫ cos x sin xdx 39/I = 4 ∫ 3 4cos x − 3sin x + 1 2 x 68*/I = 3 x −3 1 0 dx ∫ dx 129/I = ∫ 4sin x + 3cos x + 5 π 3 2 0 0 (x + 1)(x + 3x + 2) 2π 1 + sin xdx 2 14/I = 100/I = ∫ 4 ∫ sin x dx 2 x +1 9 −2 69/I = ∫ x.3 1 − xdx 0 4x 1 40*/I = dx ∫ 0 130/I = 0 (x 3 + 1) dx ∫ 2 1 x x +1 3π −2 x +1 4 2 101/I = sin 2x dx ln 2 70/I = ∫ 3 ∫ dx 1 1 e x − 1dx π 41/I = ∫ 3x + 2 131/I = 0 (x 4 + 4x 2 + 3) dx π ∫ 0 1 3 0 4 15/I = dx ∫ x π x x 6 1 1 π 71*/I = ∫ sin sin 2 cos 2 dx π π 42/I = ∫ dx 1 − sin xdx 102/I = ∫ 2 sin 3 x 2 2 4 0 3 − 2x 132/I = 3 0 0 dx ∫ x π 2 (sin 2 x + 3) π 0 72*/I = 3 dx ∫ 1  + x + 1)  dx 4 2 103/I = 2+ x + 2− x ∫ ln(x 2 43/I = 16/I = cotg2x dx 0 ∫ 5 π −1   ∫ sin xdx   3 4sin 3 x π 0 33 133/I = dx 2 ∫ 1 + x dx 6 73/I = x sin x π ∫x. π 1 − cos x 104*/I = ∫ dx π 0 2 0 1 + cosx 1 3 44*/I = 6 dx 1 ln(1 + x) ∫ π π cos x 1 1 74**/I = ∫ dx 0 = −∫1 (x 2 + 1)(4x + 1) dx 105*/I x2 +1 2 sin 2 x 1 3 0 17/I = ∫e sin 2x dx 134/I = dx 1 e −2x ∫ π cos x.sin 2 x 45/I = π π dx ∫ −x 4 +1 sin x 0e 1x 4 2 75/I = 6 106*/I = dx dx ∫ ∫ π sin x + cos x x π −1 1 + 2 1 ln 3 0 tgx + 2 dx e 46/I = ∫ 4 18/ I= 3 135/I = ∫ sin x.tgxdx eπ ∫ ex + 1 π2 0 cos 2 x 76/I = cos(ln x)dx 0 0 ∫ 107/I = 4 π x sin xdx 1 ∫ π π 1 4 0 1 2 1 2 47/I = dx 3 ∫ 2 4 + x dx 19/ I = dx20/ I = 77*/I = 136/I = dx ∫ 2 ∫ ∫ sin x cot gx π π2 sin 4 x sin 2x π π 0 6 108/I = 4 4 4 x 2 x cos xdx ∫ e ln x 32 + ln 2 x 78/I = ∫ dx π π 48/I = 0 1 1 + x −1 dx sin 3 x ∫ 1 4 dx 4 137/I = x π dx 1 ∫ ∫ cos6 x 1 + 3ln x ln x (tg x + 1)2 .cos5 x 2 e 0 6 109/I = 0 79/I = e sin(ln x) 2 dx ∫ x.sin x cos xdx ∫ 49/I =∫ dx x π 1 0 x 1 1 3 3 2x 138/I = 2 dx − x)dx 80/I = 13 xe ∫ 1 ∫ ln(x (x 4 − 1)5 dx sin 2 x + 9 cos 2 x 110*/I = ∫ 50/I = ∫ x dx π 2 − 2 + 2) 0 (x 0 3 1
  2. 2 x −1 2 x +1 7 π x 2ex 2 1 197/I = 253/I = ∫ 3 ∫( ) dx dx 2 cos x − 1 x +1 168/I = ∫ dx 226/I = 3 −1 x + 2 3x + 2 139/I = dx dx 2 + 2) ∫ ∫ 0 0 (x π cos x + 2 3 3x + 1 0 π − π e 2 cos x + sin x π ∫ (1 + x) ln x dx 4 169/I = 198/I = 3 2 ∫ x.tg x dx 254*/I = dx 2 1 + sin 2x + cos 2x ∫ π 1 3 + sin 2x 227/I = dx 0 2 1 + sin x π ∫ 140/I = cos x + sin x dx e π ∫ 4 170/I = ∫ x ln 2 x dx 5 0 1 + 3cos x + 2 − x − 2 ) dx 199/I = ∫ (x 6 π 1 −3 π 1 (1 + e x ) 2 2 3 1 ∫ cos x cos x − cos 255/I = xdx 228/I = cos x dx 2 141/I = ∫ 2 4 171/I = e2 dx 2x π 0 1+ e ∫ 200/I = dx ∫ ∫ ln x dx − sin x + cos x + 1 x+5+4 0 2 −1 1 32 (1 − x)3 dx π 229/I = ∫ x 1 4 x 2 e dx 142/I = ∫ 201/I = ∫ dx 172/I = ∫ x(2 − ln x) dx 34 0 2 x (x + 1) 256/I = ∫ tg xdx x+2 + 2−x 1 1 1 π π sin x.cos3 x 1 2 ln(1 + x) 1 e2 2 230/I = 1 1 4 dx 202/I = dx dx ∫ 143/I = 173/I = − ∫ ∫ ∫( )dx x2 cos 2 x + 1 x + 4 + (x + 4)3 π −3 2 ln x 1 0 e ln x 2 1 + sin x x 257*/I = π 1 e dx ∫ 2 π 174/I = ∫ (x 2 + x) ln x dx 0 1 + cos x 4x − 1 sin 2x sin 3 x 203/I = 2 231/I = 2 3 144/I = dx dx ∫ ∫ dx 1 ∫ 0 1 + cos x x 2 − 3x + 2 1 0 cos x (1 − x 2 )3 dx 0 258/I = ∫ 1 22 ∫ x ln(1 + 175/I = ) dx π π 0 1 2 232*/I = x sin x.cos xdx 2008 x ∫ 1 − xdx sin x 145/I = 1 ∫x 2 204/I = π dx ∫ 0 0 2 ln x sin 2008 x + cos 2008 x 259/I = 4 x.tg 2 xdx 0 176/I = dx ∫ π ∫ x−4 1 5 6 1x π cos x 146/I = ∫ 2 233/I = 0 . dx dx ∫ x+2 x+2 205/I = 2 sin x.ln(1 + cos x) dx e ln x 4 cos 2x + 7 1 2 ∫ 0 dx ∫ dx 260/I= 177/I = ∫ 1 0 1 (x + 1) 2 0 22 0 (4 + x ) 1 4 dx 147/I = ∫ dx 234/I = ∫ e −1 x 2 + 2x + 9 x2 + 1 3 x 2 (x + 1) 3x 2 206/I = 1 dx 1 ∫ 1 261/I = dx 2 ∫ 1 x 3 1+ x 1 π 2 178/I = dx x3 + 2 148/I = ∫ 0 ∫ x ln dx 2 235/I = π 2 1− x 4x − x sin 2x(1 + sin 2 x)3 dx 1 0 ∫ sin 3 x 1 − x5 4 207/I = 2 0 dx 262*/I = ∫ π dx 2 ∫ 4x − x 2 + 5 dx cos 2 x 149/I = x(1 + x 5 ) ∫ 0 x +1 2 2 1 ∫ cos x.ln(1 − cos x) dx 179/I = 236/I = dx −1 ∫ π 3 3x + 2 π π 0 2x − 5 2 208/I = 2 cos 2 x.cos 4x dx cos x 263/I = 3 dx 3 150/I = ∫ ∫ 1 dx 4 ∫ 2 x + 4x + 13 −2 dx 2 π 237/I = 0 0 1 − sin ∫ x 2 x x +9 2 sin 2 x 180/ 7 1 sin x cos3 x dx 1 1 1 ∫e π 209/I = ∫ dx dx 151/I = 0 ∫ 2 264/I = 3 sin x π 2x + ex 0 0e x 3 4 3+ e 238/I = ∫ x sin x cos xdx dx ∫ cos6 x π 0 0 ln x e 1 2 sin 2x dx 181/I= ∫ 3e4x + e2x 210/I = dx π π 2 ∫ 2 (x + 1) 152/I = 1 4 dx 3 0 1 + sin x 265/I = 6 sin x + sin ∫ x 2 3 cos x − cos xdx e 239/I = ∫ cos x dx 2x 1+ e ∫ 0 π cos 2x π 0 1 1 − 2 sin 2x 211/I = 1 dx 4 182/I = ∫ 2 dx dx ∫ 153/I = x +1 + x 1 3 ∫ 0 4 0 1 + cos x 266/I = dx x 9 + x2 1 ∫ 7 x 2 + a + x)dx x 6 (1 + x 2 ) 240*/I = ∫ ln( 1 x2 1 5 2 212/I = −1 π dx ∫ 183/I = dx ∫ π 2 04−x 2 2x − 6x + 9 154/I = π 1x 2 ∫ e sin xdx sin x 267/I = 2 1 − sin x dx 2 241/I = ∫ x 1 0 dx x 2 + 3x + 2 cos 2 x + 3 ∫ 1 213/I = ∫ dx 0 x 184/I = (1 + cos x)e dx 2 ∫ 0 04−x π x+3 π2 cos 4 x 0 sin x 2 155/I = π 268/I = 1 dx dx ∫ ∫ sin 2x + sin x 1 4 4 4 4 2 cos x + sin x 242/I = x x 2 214/I = 0 0 dx 185/I = dx ∫ ∫ dx ∫ 2 1 x (x + 1) cos 3x + 1 x2 −1 π 0 3 1 0 156/I = dx ∫ 269/I = 2 sin x cos x(1 + cos x)2 dx 1 ln(1 + x) π x+9 − x π ∫ 0 186/I = dx ∫ sin 2x 4 243/I = sin 3x 2 2 215/I = 0 0 x +1 dx ∫ dx π ∫ sin 2 x + 2 cos 2 x 157/I = ∫ x sin xdx cos x + 1 π 0 0 4 11+ x sin 4 x − cos 4 x 0 270/I = 4 187/I dx ∫ 2 dx ∫ 2 6 01+ x 3 sin x + cos x + 1 π2 x 2 2 2 244/I = 0 x 158/I = ∫ x cos xdx 2 216/I = dx ∫ dx ∫ 1 15 π 0 1 − x2 1 + x8 dx 0 2 188/I = 1− x ∫x 0 sin 4 x − cos 4 x 271/I = 4 1 0 dx ∫ 159/I = ∫ cos x dx 2 2 1 − x2 sin x + cos x + 1 0 x3 217/I = dx ex 0 2 245/I = ∫ 1 dx 4 1 1+ x 189/I = ∫ ∫ dx π 1 1 − x2 −x 0 x 272/I = 2 sin x cos x + cos x dx e +e 0 160/I = ∫ sin x dx x3 7 ∫ 0 sin x + 2 218/I = dx 1 − x2 ∫ e 0 1 3 ∫ ln x dx 0 1 + x2 dx π2 ∫ 190/I= 246/I = 2 1 1 x 2 161/I = 4 ln 2 1 − e x 1 ex 273/I = e x sin x dx ∫ 2 219/I = dx dx ∫ ∫ 3 π 0 x x 0 1+ e a x2 1 2 sin x 191/I = 247/I = π2 dx + cos x) cos x dx ∫ ∫ (e x 3 + 2x 2 + 10x + 1 1 1 4 − x2 1 − x dx 0 220/I = ∫ x 274/I = ∫ 162/I = dx 0 4 x cos x dx x 2 + 2x + 9 ∫ 0 0 π 1 2 0 dx sin 2x.cos x 1 ∫ 2 x3 192/I = 248/I = x 2 + 1 dx 1 221/I = ∫ dx x x2 −1 π ∫ 2 275/I = ∫ dx 2 1 + cos x 163/I = ∫ x cos x sin x dx 2 + 1)3 0 0 0 (x 3 0 π π 1 3 1 x 5 (1 − x 3 )6 dx π sin 2x + sin x 249/I = ∫ 2 2 193/I = 222/I = 276/I = ∫ dx 3 + sin 3 x) dx dx ∫ (cos x ∫ 6 x3 + 1 164/I = 0 2 0 1 + 3cos x ∫ x cos x sin x dx 0 0 π 0 x4 + 1 1 π x2 + 1 sin x 3 277*/I = ∫ 250/I = 2 dx 4 1 − 2sin 2 x 223/I = ∫ 4x dx dx 194/I = ∫ x6 + 1 165/I = ∫e dx dx 0 1 + sin x 0 x +1 ∫ 0 0 1 + sin 2x 1 x 1 π 1 278/I = 0 (2x + 1)3 dx π 2 2x ∫ 224/I = ∫ (1 + x) .e dx x 5 + 2x 3 cos x 3 251/I = 2 4 3x 166/I = 195/I = dx dx ∫ ∫ 0 ∫e sin 4x dx 7 + cos 2x x2 +1 0 0 1 7 π 0 279/I = ∫ dx 1 cos x 4 2 π 2 + x +1 225/I = π 2x 2 dx dx 252/I = sin 2 x dx ∫ ∫ 167/I = ∫e tgx 3 2 1 (1 + x)x cos 2 x + 1 196/I = 0 dx ∫ 0 2 cos x 1 + cos x π 4 2
  3. π π 3 cos x 1 2 2 1 2 306/I = 332/I = dx dx 280/I = ∫ ∫ dx ∫ 2 sin x 1 + cos x (1 − cos x) π π 2 x 1− x 1 3 3 2 π π x ln(x + 1 + x 2 ) 1 307/I = 4 tg3x 333*/I = 4 ln(1 + tgx)dx 281*/I = ∫ dx dx ∫ ∫ 1+ x2 0 0 0 1 4 1 2 ∫ (x − 1) ln x dx 282/I = 308*/I = dx ∫ 2x −1 3 + e 1 32 π sin 2 x ln(x + 1) dx 283/I = ∫ x 309*/I = dx ∫ x 0 −π 3 + 1 3x 3 2 π 284/I = ∫ dx sin x 310*/I = 2 2 x + 2x + 1 dx 1 ∫ cos x + sin x 0 4x − 1 1 285/I = dx ∫ π x 3 + 2x 2 + x + 2 sin 4 x 0 311/I = 2 dx ∫ 286/I = cos 4 x + sin 4 x 0 1 π 1 2 tgx 2 dx ∫ 312*/I = ∫ dx 5 + 12x + 4x 2 −1 (3 + 2x) 1 − ln 2 (cos x) 0 2 1 π 1 287/I = ∫ dx sin x 313*/I = 2 x + 1+ x dx 0 ∫ cos x + sin x 0 π cos x 1 1 288/I = 2 dx 314*/I = −∫1 (ex + 1)(x 2 + 1) dx ∫ 2 + cos 2x 0 π 1 3x +1 2 cos x + sin x 315*/I = ∫ e dx 289/I = dx ∫ 0 π 3 + sin 2x x2 1 4 316*/I = ∫ dx π x2 + 4 0 2 290/I = 3 3 ∫ (cos x + sin x)dx π cos3 x 0 317*/I = 2 dx ∫ π cos − 3cos 2 x + 3 4 0 2 291/I = 5 4 ∫ cos x sin xdx 318*/Tìm x> 0 sao cho 0 x t 2e t 292/I = dt = 1 ∫ 2 0 (t + 2) π 2 4 x + cos 4 x)dx π ∫ cos 2x(sin tan x 3 0 319*/I = dx ∫ cos x cos 2 x + 1 π π 1 2 293/I = 4 dx ∫ 2 + sin x 1 0 −3x 2 + 6x + 1dx 320*/I = ∫ π 0 1 2 294/I = π dx ∫ 2 − cos x 321*/I = 4 tg5 x 0 dx ∫ 1 0 2 dx ∫ 295/I = π x x2 −1 2 4 3 322/I = 3 ∫ cotg x dx π x3 7 296/I = 6 dx ∫ 3 0 1 + x2 π 34 1 323/I = 2 ∫ tg x dx dx 297*/I = 1 ∫ π x 1 + x3 4 π x3 1 298/I = ∫ dx 1 4 324*/I = dx ∫ x + 1 + x2 0 0 2 + tgx 1 1 π dx 299/I = −∫1 sin 5 x 325/I = 2 1+ x + 1+ x2 dx ∫ 0 cos x + 1 π 1 π 3 300/I = dx ∫ cos 2x 3 sin 4 x cos x π 326/I = dx ∫ π 1 − cos 2 2x 6 6 π cos x π 2 301/I = dx ∫ 4 t gx − 1 2 327*/I = cos x + 1 ∫( ) dx 0 0 tgx + 1 π cos x 2 302/I = x 1 dx ∫ dx ∫ 328*/I = 1 2 − cos x x3 + 1 0 π 2 sin x 303/I = 2 23 x − x3 dx ∫ 329*/I = 0 sin x + 2 dx ∫ x4 1 π cos3 x ex ln 3 2 304/I = dx dx 330/I = ∫ ∫ cos x + 1 0 (e x + 1) e x − 1 0 π π −1 1 2 305/I = e4 dx 1 ∫ 331/I = 2 cos x + sin x + 3 dx ∫ 0 x cos 2 (ln x + 1) 1 e 3
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