Đề ôn tập Chương 3 Giải tích lớp 12 năm 2021 Trường THPT Quốc Trí

A. \(\int {{{\rm{e}}^x}\sin x{\rm{d}}x}  = {{\rm{e}}^x}\cos x - \int {{{\rm{e}}^x}\cos x{\rm{d}}x} .\)

B. \(\int {{{\rm{e}}^x}\sin x{\rm{d}}x}  =  - {{\rm{e}}^x}\cos x + \int {{{\rm{e}}^x}\cos x{\rm{d}}x} .\)

C. \(\int {{{\rm{e}}^x}\sin x{\rm{d}}x}  = {{\rm{e}}^x}\cos x + \int {{{\rm{e}}^x}\cos x{\rm{d}}x} .\)

D. \(\int {{{\rm{e}}^x}\sin x{\rm{d}}x}  =  - {{\rm{e}}^x}\cos x - \int {{{\rm{e}}^x}\cos x{\rm{d}}x} .\)

A. -2

B. 2

C. 3

D. 4

A. \(S = \frac{7}{3}\)

B. \(S = \frac{8}{3}\)

C. S = 7

D. S = 8

A. F(9) = -6

B. F(9) = 6

C. F(9) = 12

D. F(9) = -12

A. \(F\left( 3 \right) = \ln 2 - 1\)

B. \(F\left( 3 \right) = \ln 2 + 1\)

C. \(F\left( 3 \right) = \frac{1}{2}\)

D. \(F\left( 3 \right) = \frac{7}{4}\)

A. -13

B. -7

C. 13

D. 7

A. \(F\left( x \right) = \frac{{{{\left( {3x + 1} \right)}^6}}}{{18}} + 8\)

B. \(F\left( x \right) = \frac{{{{\left( {3x + 1} \right)}^6}}}{{18}} - 2\)

C. \(F\left( x \right) = \frac{{{{\left( {3x + 1} \right)}^6}}}{{18}}\)

D. \(F\left( x \right) = \frac{{{{\left( {3x + 1} \right)}^6}}}{6}\)

A. \(y = 12{x^6} + 5\)

B. \(y = 2{x^6} + 3\)

C. \(y = 12{x^4}\)

D. \(y = 60{x^4}\)

A. \(\int {0\,{\rm{d}}x}  = C\)

B. \(\int {{x^4}\,{\rm{d}}x}  = \frac{{{x^5}}}{5} + C\)

C. \(\int {\frac{1}{x}} \,{\rm{d}}x = \ln x + C\)

D. \(\int {{{\rm{e}}^x}} \,{\rm{d}}x = {{\rm{e}}^x} + C\)

A. \(S = \frac{{10}}{3}\)

B. \(S = \frac{8}{3}\)

C. \(S = \frac{{13}}{3}\)

D. \(S = \frac{5}{3}\)

A. (II) và (III)

B. Cả ba mệnh đề

C. (I) và (III)

D. (I) và (II)

A. \(F\left( a \right) - F\left( b \right) = \int\limits_a^b {f\left( t \right){\rm{d}}t} \)

B. \(\int\limits_a^b {f\left( t \right){\rm{d}}t}  = \left. {F\left( t \right)} \right|_a^b\)

C. \(\int\limits_a^b {f\left( t \right){\rm{d}}t}  = \left. {\left( {\int\limits_{}^{} {f\left( t \right){\rm{d}}t} } \right)} \right|_a^b\)

D. \(\int\limits_a^b {f\left( x \right){\rm{d}}x}  = \int\limits_a^b {f\left( t \right){\rm{d}}t} \)

A. 3

B. 0

C. 2

D. 1

A. \(\frac{{ - {x^4} + {x^2} + 3}}{{3x}} + C\)

B. \(\frac{{ - 2}}{{{x^2}}} - 2x + C\)

C. \( - \frac{{{x^4} + {x^2} + 3}}{{3x}} + C\)

D. \(\frac{{ - {x^3}}}{3} - \frac{1}{x} - \frac{x}{3} + C\)

A. \(\int {f\left( {ax + b} \right){\rm{d}}x}  = \frac{1}{a}F\left( {ax + b} \right) + C\)

B. \(\int {f\left( {ax + b} \right){\rm{d}}x}  = \frac{1}{{a + b}}F\left( {ax + b} \right) + C\)

C. \(\int {f\left( {ax + b} \right){\rm{d}}x}  = F\left( {ax + b} \right) + C\)

D. \(\int {f\left( {ax + b} \right){\rm{d}}x}  = aF\left( {ax + b} \right) + C\)

A. \(f\left( x \right) = \frac{{{x^2}}}{2} - \cos x + 2\)

B. \(f\left( x \right) = \frac{{{x^2}}}{2} - \cos x - 2\)

C. \(f\left( x \right) = \frac{{{x^2}}}{2} + \cos x\)

D. \(f\left( x \right) = \frac{{{x^2}}}{2} + \cos x + \frac{1}{2}\)

A. \(S = 4\ln 2 + {\rm{e}} - 5\)

B. \(S = 4\ln 2 + {\rm{e}} - 6\)

C. \(S = {{\rm{e}}^2} - 7\)

D. S = e - 3

A. \(S = \int\limits_a^b {\left| {{f_1}\left( x \right) - {f_2}\left( x \right)} \right|{\rm{d}}x} \)

B. \(S = \int\limits_a^b {\left( {{f_1}\left( x \right) - {f_2}\left( x \right)} \right){\rm{d}}x} \)

C. \(S = \int\limits_a^b {\left| {{f_1}\left( x \right) + {f_2}\left( x \right)} \right|{\rm{d}}x} \)

D. \(S = \int\limits_a^b {{f_2}\left( x \right){\rm{d}}x}  - \int\limits_a^b {{f_1}\left( x \right){\rm{d}}x} \)

A. \(\frac{2}{{\ln 3}}\)

B. 2ln3

C. 1,5

D. 2

A. \(\frac{1}{8}.\sqrt[3]{{({x^2} + 1)}} + C.\)

B. \(\frac{3}{8}.\sqrt[3]{{({x^2} + 1)}} + C.\)

C. \(\frac{3}{8}.\sqrt[3]{{{{({x^2} + 1)}^4}}} + C.\)

D. \(\frac{1}{8}.\sqrt[3]{{{{({x^2} + 1)}^4}}} + C.\)

A. \(I = \frac{\pi }{4}\)

B. I = -1

C. I = 0

D. I = 1

A. \({x^5} + 2x + C\)

B. \(\frac{1}{5}{x^5} + 2x + C\)

C. 10x + C

D. \({x^5} + 2\)

A. \(5\cos 5x + C\)

B. \( - \frac{1}{5}\cos 5x + 2x + C\)

C. \(\frac{1}{5}\cos 5x + 2x + C\)

D. \(\cos 5x + 2x + C\)

A. \(\frac{{{x^4}}}{4} - 1\)

B. \(3{x^2}\)

C. \(\frac{{{x^4}}}{4} + 1\)

D. \(\frac{{{x^4}}}{4}\)

A. \(V = \pi \int\limits_1^3 {{{\left[ {f\left( x \right)} \right]}^2}{\rm{d}}x} \)

B. \(V = \frac{1}{3}\int\limits_1^3 {{{\left[ {f\left( x \right)} \right]}^2}{\rm{d}}x} \)

C. \(V = {\pi ^2}\int\limits_1^3 {{{\left[ {f\left( x \right)} \right]}^2}{\rm{d}}x} \)

D. \(V = \int\limits_1^3 {{{\left[ {f\left( x \right)} \right]}^2}{\rm{d}}x} \)

A. \(\int\limits_a^b {f\left( x \right){\rm{d}}x}  - \int\limits_b^c {f\left( x \right){\rm{d}}x} \)

B. \(\int\limits_a^b {f\left( x \right){\rm{d}}x}  + \int\limits_b^c {f\left( x \right){\rm{d}}x} \)

C. \( - \int\limits_a^b {f\left( x \right){\rm{d}}x}  + \int\limits_b^c {f\left( x \right){\rm{d}}x} \)

D. \(\int\limits_a^b {f\left( x \right){\rm{d}}x}  - \int\limits_c^b {f\left( x \right){\rm{d}}x} \)

A. \(- 3\sin x + \frac{1}{x} + C\)

B. \(3\sin x - \frac{1}{x} + C\)

C. \(3\cos x + \frac{1}{x} + C\)

D. \(3\cos x + \ln x + C\)

A. 101376

B. \({{\rm{e}}^2}{\rm{.}}{x^{{\rm{e}} - 1}} + C\)

C. \(\frac{{{x^{{\rm{e}} + 1}}}}{{{\rm{e}} + 1}} + 4x + C\)

D. \(\frac{{{\rm{e}}{\rm{.}}{x^{{\rm{e}} + 1}}}}{{{\rm{e}} + 1}} + 4x + C\)

A. \(3\ln 2 - 1\)

B. \(3\ln 2 \)

C. \(3\ln 2 - 2\)

D. \(3\ln 2 - 3\)

A. \(\frac{{96}}{{64}}\)

B. \(\frac{{97}}{{64}}\)

C. \(\frac{{67}}{{64}}\)

D. \(\frac{{99}}{{64}}\)

A. \(\frac{7}{2}\)

B. \(\frac{9}{2}\)

C. \(\frac{5}{2}\)

D. \(\frac{3}{2}\)

A. \(\frac{{11}}{5}\)

B. \(\frac{{12}}{5}\)

C. \(\frac{{13}}{5}\)

D. \(\frac{{14}}{5}\)

A. 4

B. 6

C. 8

D. 10

A. \(\frac{{{e^2} + 1}}{2}\)

B. \(\frac{{{e^2} - 1}}{2}\)

C. \(\frac{{{e^2} + 1}}{4}\)

D. \(\frac{{{e^2} - 1}}{4}\)

A. \(\frac{{e - 1}}{2}\)

B. \(\frac{{e + 1}}{2}\)

C. \(\frac{{e - 1}}{4}\)

D. \(\frac{{e+ 1}}{4}\)

A. \(\frac{{34}}{{15}}\)

B. \(\frac{{36}}{{15}}\)

C. \(\frac{{38}}{{15}}\)

D. \(\frac{{39}}{{15}}\)

A. \(\frac{{38}}{{15}}\)

B. \(\frac{{38}}{{10}}\)

C. \(\frac{{38}}{{25}}\)

D. \(\frac{{38}}{{35}}\)