Tinh tich ab.. Cong thuc nao sau day sai?. Tim tQa dQ cua vect... fJxdx =f Judu... Khing djnh n4o sau d4y la khing djnh sai?
Trang 1I Stl GD&OT TP f-IA N()t
TRU"ONGTHPTTA¥ 86
DE KltM TRA THU' GIO'A HKll ' , NAM HQC 2020 - 2021 :
(DJ tJu c6 0 7 tra,ig)
MON TOAN - Kb61 lap 12
Th<1i gian lam bai : 90 phut
(khong ti thoi gian phdt di)
(;ju J Ti'm cAc ham ~ / (J\·) biet rffng / '(x) = (2 +smx co~x )2 \ \ ' \
A / .t) "" 2+ c.osx + C B X = ( 2+cosx )2 +
Clu 1 Cho ham sA /(x) Ii~ t\10 tr6n (a;b] H!ly chQn m~ dA said~ dAy:
A J /(x)d'C=-J / (x)dl'
, B J f(:c)dx = J /(x)dx
C J /(x)<h-= J /(;\·)dx+ J /(x)dxv(ri ce[a;b]
t
Ci• 3 Tim nguy6n ham J = I l+e dx
A J =-x- tn\l+if' \+C ~- /=x-Inlt+e l+C
'-i ,\ \
C / =.r-ln/1-e /+c D / = ~+Inlt+e l+C
Ci•'- Cho biet f f(x)dx=2, f g(x)dx = - 3 Gia tri cua M = f[sJ(x)+3g(x)]dx bing
Ciu 5 Kit qua cua J 1n xcu- la
Ciu 6 Ham sA nao sau day la nguy~n ham cua ham s6 y = - ? e +1
A F ( x) = e + 1 -ln ( e., + 1) + C B F ( x) = ex + In ( e., + 1) + C t
-C F ( x) = e11 - In Ix!+ C D F ( ~) = i' + In jxj + C
\
c, 7 Cho bai ham s6 y = I( x) va Y = g( x) li&l t\lC tr!n do(Ul [ a;b] OQi D la hlnh ph!ng gi6i h{Ui boi
cacda thi ham sA y= f(x),y=g(x)va hai d\rong thing x=a,x=b (a >b)di~n tfch cua D ·duc;,c theo :::~
~ngthuc
•
A JIJ (x)-g(x~dx
•
b
B f{J(x)-g(x))dx
II
C S = f /(x)<ix-J g(x)dx
II
D JIJ(x)-g(x~dx
•
Cl~ 8 "frong kbong gian voi M tr\lC tQa d~ Ol.J,z, cho Mn di&11 A(2; - 3;7), B(0;4;1), C{3;0;5) vt\
Trang 2D(3;3;3) GQi M la di~m n~ tren m~t phfulg (Oyz) sao cho bi~u thuc IU4 rt- MB+ MC+ MDj d~t gia tri
nho nhit Khi d6 tQa de) cua M la:
A M(0;l;-2) B M(0;l;4) C M(2;1;0) D M(O;l;-4)
Ciu 9 Cho hai tich phan J f(x)dx =8 va J g(x)dx= 3 Tinh I= J[J(x)-4g(x)-t}ix
- 2 S - · -2 '8
A I = 21- B: / = 13 C / = 3 - D J = -11 ·
Ciu 11 Biet nguyen ham F(x) cua ham s6 f x.e.r'+tdx va F(0) =ie Tinh F(l)
2
1
Cau 12 Nguyen ham cua ham s6 y = -e"'sx sin x la
A y=eoosx B • Y = -e sinx C Y = eSID., • ·
Cau 13 Bi~t f xe 2 ,.dx = axeix + beix + C ( a, be Q) Tinh tich ab
A ab - 8 B ab = -8 C ab= - 4
D y=-eoosx
I
D ab=
4
Ciu 14 Cho J cos2x 3 dx =
(sinx+cosx+ 2)
( sin X + cos X + l r
(smx+cosx+2 )" +C v6i m,neN Tinh A=m+n•
A A= 2 B A= 3 C A=5• D A=4•
Cau 15 Cong thuc nao sau day sai?
A J-\-dx=tanx+C
COS X
B J-!·dx=Inl~+C
X
C Jsin2xdx=-½cos2x+C D f lnxdx=.!.+c
X
Cau 16 Voi bai toan "Tun f ':°~x dx ", biµi An th\lc hi~n giai bing phuang phap d6i bien s6 nhu sau:
Buoy l: D~t u = sinx, ta c6 du= cosxdx
sin2 x u 2 u
· Bu6c 3: Ket luan , I dx cosx = +C 1
sin2 X X
Theo thu tµ tren xu6ng, biµi An bAt dAu sai tir bu6c nao?
A Bu6c 3 B Bu6c 1 C Khong sai D Bu6c 2
Cau 17 Trong khong gian v6i M tQa de) Oxyz, cho hinh vuong ABCD, B(3; 0;8), D(-5;-4; 0) Bi~t dinh
A thuQC m~t phing ( Oxy ) va c6 tQa dQ la nhiing s6 nguyen, khi d6 lcA + CBI bing:
2/6- Mad~
Trang 3J J
C'iu 18 Cho f f(x};L~ • a J /(x)d.x "" b Khi d6 j /(:i)dx blJta:
A-b - u - B _ _ a b · C a - b D a + b
Ciu 19 Tmng kM • " · nggJanvvd~tQad~ 0-ty:,chotamgiac · A.! ABC co A(0;t;4) , 8(3;- 1;1) , C(-2;3;2)
Clu 20 nm nguyl-.n ham cua ham sA / ( x) (3 - 2.x)'
A l~ (l - 2x}6 +C B - /
2 (3 - 2x}4 +C
Cla 11 Tun nguyen ham cua ham sA / ( x) = 1n x
C !_(3 - 2xf +C
12 D _ !_(3-2x)' +C 12
A /(x)d'.t =
9x' (3lnx - 2)+ C B J /(x)dr =¾xi (31n x- l) +C
C J / (x)dx =
9x1 (31nx - 2)+C D J /(x)cir=
3x2 (31nx -2)+C
Cio ll Trong khong gian v6i h~ tQadQ Oxyz, cho hinh binh hanh ABCD voi A(l;l;-5), B(2;1;-3),
C (0-,-2;5) Dinh D c6 tQa dQ h\
,
'
Ciu 24 Bih f f(x)dx =-2; f f(x)dx = 3; J g(x)dx = 7 M~nh d8 nao sau day sai?
•
A f f(x)dx=-5
4
'
B J[J(x)+g(x)]cir=IO
I
'
C J[ 4/(x)-2g(x)]cir =-2
I
•
D J /(x)dr=l
'
dum day la m<,t vecta phap tuySn cua mtt phlng (ABC)?
A ni = l;2;5 B = I;-2;5 C = ;-2;-5
Ciu 26 Bi€t / = j 2!x- 2I+ 1 cir =
4+aln2+bln5 voi o,b e Z Tinh S = a +I,
I X
A S = 5 • B S = 9 - C S =-3 D S=tl
x+2y-3z+ l = 0 va 2x -3y +t+l=0 cophuongtrlnhla
A x + y + z + 2 = O B x - y + z - 6 = 0 C 2x + y + z - l ,, 0 D x + y + : - 2 = I)
Ciu 28 Bi€! J x cos 2xdx = ax sin 2x + b cos 2x + C v6i a , b la cAc s6 hOu ti Tlnh ticb ab ?
Trang 41
C ab =s·
l
D ab=- 4·
A ab = _]_ B ab = _41 •
3
A -+ e B F e = -
A Jkcix=k(a-b), 'v'ke R.• B JJ(x)dx= f f(x)dx+ f J(x)dx, 'vce(a;b •
C J /(x)dx = -J J(x)dx D J /(x}dx = J /(t}dt
Ciu 31 Trong kbong gian v6i M tr\lC tQa dQ ~ , cho vecta ii= (1;-2;3) Tim tQa dQ cua vect<Y b biet ring vecta b nguc;rc huong v6i vecta a va IEI = 21a1
b a b a
1) J f(x)dx=-f f(x)dx 2) f2J(x)dx=2f J(x)dx
3) !/2(x)dx= f J(x)dx 4) [f(x)dx= [f(u)du
1-Cau 33 Trong khong gian v6i he tQa dQ Oxyz , cho di~m · A ( 1; -1; 1) va m~t ph!ng
A F(4)=2.;i_i_ B F(4}=4e2+3 C F(4)=3 D F(4)=4e2
-3
4 4
Tinh gia tri cua bi~u th(rc p = a+ b + C •
4/6- Mad~
Trang 5a •
r f f (x)dx= - JJ (x)dr 2· J2/(x)dx = 2J b a f(x)dx
4 fJ(x)dx =f J(u)du
a a
Ciu 38 Trong khong gian Ox_J,zcho ba di~m A(l;2;3), B(3;4;4), C(2;6;6) va I(a;b;c) IA tam duong
tron ngo{li tiq, tam giac ABC Tinh a+ b + c
46
B.-
~-3
D 63
5
5
Ciu 39 Cho F(x) =(ax2 +bx-c )e2z la mQt nguyen ham cua ham s6 /(x) = (2018x2 -3x+l)e2" tren
khoang (-«>; +oo) Tinh T = a+ 2b + 4c
A T=lOll· B T=l007• C T=-3035• D T=-5053·
Ciu 40 Ham s6 c6 mQt nguyen ham la F(x) N~u F(O) =2 thi F(3) bkg
A 886 B 3 C 146 D ~
Ciu 41 Nguyen ham cua ham sA y = cos2
x.sin X la
1 3
1 3 C
-sm x+
3
I 3
3
D -cos3 x+C
A F(x)=ln l+Jl
C F(x) = 1njcos2 ~
ml2+sin2 xi
D F(x)= ' ~'
3
Ciu 43 MQt nguyen ham cua ham s6 f(x) = + x 2 la
3
I = f f'(x)dx
Ciu 45 Tfnh difn tfcb mi~n blnh phing gi6i hfD bcn cac 4U'O'Dg y = x 1 - 2x, y = 0, x = -l O, x = lo
000
A f-\-dx= tanx+C
COS X
B f sinxd:< =-cosx+C
Trang 6i
Ciu 47 Khing djnh n4o sau d4y la khing djnh sai?
A (I f(x)ix)' = J(x),
B f kf(x)ix = f /(x,ixvm ke R,
a+l
Ciu 48 Tfnh di~n tich S cua hlnh piling gi6i b6i cac duong y = x2, y = 2x2 - 2x ?
D(2;1;-2) Khi d6 th~ tfch tu di~n ABCD la
A V = - B V = - C V = - D V = -
Cau 50 GQi S la di~n tich mi~n hinh phAng du.;rc to~ trong hlnh v~ ben Cong thuc tinh S la
l 2
A S= /f(xJtx-ff(xJJx
2
B S = f f(x)ix
I 2
C S = J /(x)ix+ J f(x)ix
- 1 I
- I
2
D S=-J /(x}ix
- I
y
H t T
-6/6-M!d~
' t