Cac cong thuc tich phan

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    31-Jul-2015

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1. CONG THC TCH PHANCONG THC C BAN CONG THC M RONGdx = x +Cdu =u +C x +1u +1 x dx =u du = +C +C +1 +1dx 1 1x = ln x + C (ax + b) dx = a ln ax + b + C1 ( ax + b )n +111 (ax + b) dx =+C u dx = u n dx = +Cna n +1 n ( n 1).u n 1e dx =e x +C x1 ax + b au e dx = + C ; a u du = ax + be+Caxa ln u a dx =+C x 1 ln asin(ax + b)dx = a cos(ax + b) + Ccos x.dx =sin x +C; 1 1cos(ax +b)dx = a sin( ax +b) +C cos(nx).dx = n sin nx + C u dusin x.dx =cos x +C ; u dx = u = ln u + C ;1 u u 1 sin nx.dx = n cos nx + C u dx = 2 u + C ; u 2 dx = u + C 1 cosx2dx = (1 + tg 2 x ) = tgx + C 1 sin 2 x dx = (1 + cot gx) = cot gx + C 2CAC PHNG PHAP TNH TCH PHANb f ( x) = F ( x) bI/ CONG THC NEWTON LEPNIC: a = F (b) F ( a )aII/ PP OI BIEN :bDANG I : f ( x).dx = f (( x)). ( x).dxa; Vi ( a ) = ; (b) = b* Cach lam : at t = x ) . oi can . (I = f ( x).dx = g (t ).dta + Lay vi phan 2 ve e tnh dx theo t & tnh dt . + Bieu th : f(x).dx theo t & dt .(f(x)dx= g(t) dt )DANG II : at x = ) . (Tng t tren ). (tIII/ PP TCH PHAN TNG PHAN :b b* Cach lam :bieu dien f(x)dx ve dang tch u.dv =u.dv =u.v v.dub a u.vdx.a a+ chon u sao cho du de tnh . + chon dv sao cho de tnh v = dv . + ap dung ct . 2. sin ax sin ax b cos ax c osaxDANG I :a tgax p(x). dx ;Th at u = p(x) : a thc ;dv = tgax dx suy ra v . ax ax e e bDANG II : p( x). ln x.dxa; Th at u = lnx ; dv = p(x).dxMOT SO DANG TCH PHAN THNG GAPI/ Tch Phan ham Hu T :bP( x) I= Q( x) dxa; * Cach lam :1 1Lu y CT: (ax + b) dx = a ln ax + b Neu bac t nho hon bac mau :11 u ndx = ( n 1).u n 1 + Phan tch:P( x) ABCx + D=++Q( x) x ( x ) 2ax 2 + bx + c+ ong nhat 2 ve ang thc tm A,B,C,D va a vet/phan c ban Neu bac t ln hn mau th chia a thc va ave dang tren .II/ Tch Phan Ham Lng Giac :bb 1. af (sin x ). cos xdx ; oi bien t = sinx . 2. f (cos x). sin xdx a; oibien t = cosx .b 3. f (tgx )dxa ;oi bien t = tgx . 2 1 + cos 2 xb cos x = 2 f (sin 2n 4. x, cos 2 n x) dx ; Dung CT ha bac :a sin 2 x = 1 cos 2 x 2b1 5. sin ax. cos bx.dx ; Dung CT : sin A. cos B = 2 [sin ( A + B ) + sin ( A B ) ]ab1 sin ax. sin bx.dx ;sin A. sin B = [cos( A B ) cos( A + B ) ]a 2 3. b 1 cos ax. cos bx.dx; cos A. cos B =[cos( A + B ) + cos( A B ) ]a2bdxx2t 6. a cos x + b sin xa;oi bien t = tg 2 . Th sinx = 1 + t 2 ; cosx =1 t 21 +t 2.III/ Tch Phan Ham Vo T : b ax + b ax + b Dang 1. f ( x, n cx + d).dx ;oi bien t =ncx + d giai tm x = ) .Tnh(t adx theo dtb Dang 2. f ( x,aa 2 x 2 ).dx ; oi bien x= asint ; Tnh dx theo dt .b a Dang 3. f ( x,ax 2 a 2 ).dx ; oi bien x = sin t ; Tnh dx theo dt .bbdxdx Dang 4. x 2 + a 2; Hoac : a x +a2 2; oi bien x = atgt ; Tnh dxatheo dt . 21IV/ Tch Phan Truy Hoi : ( 1 + tg x = cos 2 x )b Cho In = f (n; x)dx .Vi nN.Tnh I1; I2.Lap cong thc lien he gia In & Ina+1 . Suy ra In