F u s m o n o V, R. I s o m o V, B. X o ‘ j a y e V matematikadan
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/ _ е 1 г~ 5 - m i s o l . У ~ i+e' ' d iffe ren sial ten g lam an in g >(0) = V 2 bosh lan g 'ich sh artn i q a n o atlan tiru vch i xususiy yechim ini toping. Y e c h i l i s h i . у = ^ deb, tenglam aning o 'zg a ru vch ila rin i aj- ra tam iz: Integrallab, umumiy yechimni hosil qilamiz: 2 =ln(l + ex) + C, bunda 2C = In С desak, у = ^2lnC■(\ + e x ). Bu umumiy yechimga x = 0 , у = \[2 ni qo‘yib, С = ^ ekanligini topamiz. Izlanayotgan xususiy yechim y = ^ 2 \ n e 2 (\+ex) ko‘rinishda boiadi. J a v o b : V = J 2 In ^ (1 + e x) . M ustaqil ishlash uchun test topshiriqlari 1 .f( x) = 5x4 + 3x 2 funksiyaning boshlang'ich funksiyasini toping. A ) ^ + ^ + C; B) x 5 + x3 +C; C ) ^ + | + C ; D) x 4 +x3+ С; E) -*3 + *3 + C. 4 4 2. / (x ) = 4л/х - 6Vx funksiyaning boshlang'ich funksiyasini to ping. A ) 1 2xlfx - 1 2 х л / х + C ; В) у - х л / х - 9 x + x 3 a/x + C ; 438 С) 3x\fx - 4x\fx + С; D) 3\[х" - 4 л/х + С; Е) 4х\/х + 2ху[х + С. 3. f ( x ) = e 5 +cos2.v funksiyaning boshlang'ich funksiyasini to ping. A) 5e5 + -|sin 2x + C; B) + sin 2x+ C ; C) + isin .r + C; D) 5e 5 + -^cos2x; E) e* + 2 sin 2 x + C ; 4. /(x) = -2 s in (2 x - l) funksiyaning boshlang'ich funksiya sini toping. A) x - 2 - 2co s(2.y - 1) + С; B) ln (x - 2) + 2 c o s (2 x - 1) + C; C) x - 2 + 2cos(2x - 1) + С D) ln(x - 2) + cos(2x - 1) + C; E) -2 1 n (x -2 ) + co s(2 x- 1) + C. 3 v - — 5. f ( x ) = 7 cos у + 3e 2. funksiyaning boshlang'ich funksiya sini toping. 3 v - — 3 jr_L A) 7 sin y + 3e" 2 +C; B) 49 sin у -l-e" 2 +C; C) -4 9 sin y + e '' 2 +C; D) - I s i n ^ + e ’* 2 +C; E) sin^ + Z ' 4 + с. 6. f ( x) = y[x funksiya uchun grafigi M(9;10) nuqtadan o'tadigan boshlang'ich funksiyasini toping. A) | x V x - 8 ; B) j x\fx +18 ; C) yx\lx + 27; D) ^\fx+ 8 ;E ) ^ x V x -8 . 7./(x) = sin2x funksiya uchun grafigi M ^ ;5 j nuqta orqali o'tuv- chi boshlang'ich funksiyani ko'rsating. 4 3 9 А) - j cos 2x + 4,5 В) 2 cos 2x + 4,5 ; С) \ cos 2x - 4,5 ; D) - cos2x + 6 ; E) cos2x - 6 . 8 ./ {x) = cos2x funksiyaning boshlang'ich funksiyasini toping. A) co*3 v + С; B) sin2x + С; C) j sin 3 x + C; D) j * + 4 s *n + С ; E) |.v + 2 s m 2 .t + C ; 9 ./ (. y ) = tg2.Y funksiyaning boshlang'ich funksiyasini toping. 3 A) tg^ ' + С; B) In cosx + С; C) tg - x + C; D) ctg3x + C; E) tg2x - x + C. 10. v = 2 sin 5x + 2 cos * funksiyaning x = ^ da 0 ga teng qiy- matni qabul qiladigan boshlang'ich funksiyasini toping. A) 4 sin 2 “ 5 cos5x -1 ,8 ; B) sin * - 10cos5x + 4,5; C) 6 sin 2 - 2 c o s 5 x - 2,8; D) 6 sin cos5x + 2,8; E) 4sin 2 “ 5 cos5x + 1,8. И- f i x ) = ( 5 ' — 1)(5 v + l) funksiya uchun grafigi koordinata boshidan o'tadigan boshlang'ich funksiyasini toping. A) 2 ■ 5X In 5 - 2 In 5; B) (5 V - 5_Jt) In 5; С) 5 ' -1 + 5 - f- ' ; D) 2 ■ 5 v In 5 - 2 ; E) 5't+15“A“ 2 . ’ In 5 7 In 5 12. / ix) = -——-— funksiyaning boshlang'ich funksiyasini to ping. A ) 3 2 l l n 3 2 ^ 2 i l n 2 + C ; B) f + 2“O ln 2 + C; 4 v In 4 { i J C) f * 3 + C :D ) *‘ ; - 3 J + C ;E ) ? + r 2 -3 In 2 2 '3 1 n 2 1 \ In 2 + С 4 4 0 13. f ( x ) = C°S^ 5 yS6x funksiyaning boshlang'ich funksiyasini toping. А) - +C; B) - ! sin4x + \ co s6 x - * cos5.v + C; cos‘ ,v sin“ .r 4 6 5 C) - 2 cos.v + C; D) - 2 cos2.v + С; E) - 2 cos 1 Ox + C. 14*. / (x) = - ^ 2 funksiyaning boshlang'ich funksiyasini toping. А)л- + 21n(x - 2) + С; B) ^ - 2 + С; C )x - ln(x - 2) + C; D) 2x ln(x - 2) + С; E) * + C ; 2 In .Y 15*. Г x dx integralni toping. J 8+x A) ^- + ln(8 + x3) + C; B) x* +*4 +8x + C; C) ^ln(8 + x3) + C; D) } ( x 2 ln(8 + x 3)) + C; E) x 2 ln(8 + x 3) + C. Г dx 16*. J x[nx integralni toping. A ) l n - r + i + C ; B ) “ ^ + i + C ; C > x 2 + Inx + C ; D) lnjc + C; E) ln(lnx) + C. 17*. J x V ? - I d x integralni toping. A) Z + M i p Z + C; В) >/(*2" 7)3 +C; С) 2x2V u2-7)3 + c . 2 3 3 6 D) ^ i - 4 Z z Z Z + C - E) xU ( x 2 - l ) \ > 2 3 + u , 6 + c . 18*. J s i n x c o s 2 xfi/x integralni toping. A) -co sx+ — + C; B) -c o s x + sin3 X+C; C) - co* - + C; D) sin3 x + С; E) - c o s x + sin3 v + С . 441 19. J ( x - 5) sin xdx integralni toping. 2 A) (5 - x) cosx + sinx + С; B) - ^ cos x - 5 cos x + C\ C) - *2 cos x + 5 cos x + C; D) - ^ x ^ cos x + C; E) - x c o s x - 5si” * + C; 20*. | x 2 e 2xdx integralni toping. A) ^ В) ^ + С ; C ) f + 2x2 - 2x jD) ^-e2j:(2 x 2 - 2 x + l) + C; E) j, e>2 t (.*2 - * + J ) + C. 21*. J V cos xdx integralni toping. A) ^ -(sinx + cosx) + C; B) e^sinx+C; C) X X D) e (cos jc-sin x) + C; E) ^ (sin x - cos x) + C. 22*. J x l n ( 2 x)dx integralni toping. A) 1 + ln(2x) + 2x + С; В) *2 ln(2x) - * + C; C) *2 +ln(2x) + 2x+C; D) ^ ln(2x)+ ^ +C; E) X 22 ln (2 x )-X 42 +C. 2 23. J6jf5rfjc ni toping. 1 A) 63; B) 31; C) 4800; D) 1; E) 65. f 24. U 3 x - e i )dx m toping. о 442 2 5 - ni toping. о А ) { ; В) -1 ; С) 1; D )-3 Е ) - ‘ . е 26. J х In xdx ni toping. 4~e A ) ^ - J ; B ) ^ ; C ) 4 - f ; D ) e 2 - f ; E) 2e2. Л 4 27. J s i n 2 y ^ -x } d x ni toping. о A ) f + i ; B) J - J ; C) J - J ; D) ; + { ; E) f - 1 . 0 ,5 28. J esm ш cos nxdx ni toping. о A) e - 1; B) V 7 -1 ; C) ^ ~ l ; D) e~x; E) *. , 2 - l - in f 29. J X+1 m toping. о A) 3; B) -3; C )2; D )-2; E)e2 3 30*. J 3 - x dx ni toping. -l A) 2; B) 4,5; C )6; D) 7; E) 8. 2 л 31*. | sin x dx ni toping. о A )0; B) 2; С) 1; D) 3; E) 4. А) 16,5 - Зе; В) 10,5 - Зе; С) 13,5 - Зе; D) 1 6 , 5 - | ; Е) 13,5- 7Г 4 4 3 U> |< b 32. _[(-* —log2 a)dx = 21og2 tenglik a ning qanday qiymatlari- o da o‘rinli boiadi? A) (1;2); B) ( 2 ;+oo); C)(0;+oc); D) (—1;1); E) (4;32). a 33*. J ( , + 1 )dx ni hisoblang. - 2 A) 4; B) 3; C )2; D )-4 ; E )-3. 34. у - x 2 + 4 funksiya grafigi va у - 0, x = - 1, x = 1 to‘g‘ri chi ziqlar bilan chegaralangan shakl yuzini toping. A) 4 * ; B ) 8 | ; Q 8 ^ ; D )4; E) 7 § . 35. у = yfx + 1 funksiya grafigi, Ox o‘qi, x = 1 to‘g ‘ri chiziq bi lan chegaralangan shakl yuzini toping. A) 2,5; B) 2; C) 1; D) l | ; E) 3,5. 36. у = 1 to ‘ g ‘ri chiziq, Oy o 'q i va у - sinx funksiyaning 0 < x < у kesmadagi grafigi bilan chegaralangan shakl yuzini hisoblang. A) 1; B ) f ; C ) f + 1; D ) f + 2; E ) f - 1 . 37. v = 1 to‘g‘ri chiziq, у - 2cosx funksiyaning - ^ < x < ^ kes madagi grafigi bilan chegaralangan shakl yuzini hisoblang. A) 2 ( V 3 - | ) ; B) V3; С) 2л/3; D) 4 - я ; E) 4 - f . 38. у = 4 - x 2 parabola, у = x + 2 to‘g‘ri chiziq va Ox o‘qi bilan chegaralangan shakl yuzini toping. A) 4,5; B ) 6 j ; C) 2 | ; D) 4; E) 5 6 ‘ 39. у = x\ у = 2x - x 2funksiyalarning grafiklari va Ox o‘qi bilan chegaralangan shakl yuzini hisoblang. A ) £ ; В) 1; C ) ,72 ; D)|>; E) 8. 40. v = e\ у = e va x = 0 chiziqlar bilan chegaralangan shakl yuzi ni toping. 2 4 4 4 4 1. У = sin х, у = cos х,х — О^х е [^0; ^ J j chiziqlar bilan chegara langan shakl yuzini toping. A) 3 - V 2 ; B) 2 -V 2 ; С) 2-л/З; D) V 3 -1 ; E) >/2-1. 42. у = j giperbola, .v = 3, .v = 12 to‘g‘ri chiziqlar va Ox o‘qi bilan chegaralangan egri chiziqli trapetsiyani abssissalar o‘qi atrofi- da aylanishi natijasida hosil boigan jism hajmini toping. А) 4л; B) 6 j 71; С) 4,5л; D) 6,5л; E) 5я; 4 3 . у - sin.v funksiyaning 0 < л' < к kesmadagi grafigi va Ox o‘qi bilan chegaralangan shaklning abssissalar o‘qi atrofida aylanishi- dan hosil bo‘lgan jism hajmini toping. A) f ( я - 1 ) ; В) C) ^ ; D) f ( л - 4 ) ; E) Yüklə 8,88 Mb. Dostları ilə paylaş:
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