Trắc nghiệm Toán 12 Chương 3 Bài 1 Nguyên hàm

A. \(\int {f(x)dx} = \ln x - \ln {x^2} + C\)

B. \(\int {f(x)dx} = \ln x - \frac{1}{x} + C\)

C. \(\int {f(x)dx} = \ln \left| x \right| + \frac{1}{x} + C\)

D. \(\int {f(x)dx} = \ln \left| x \right| - \frac{1}{x} + C\)

A. \(f(x) = {x^2} + x + 3\)

B. \(f(x) = {x^2} + x - 3\)

C. \(f(x) = {x^2} + x\)

D. \(f(x) = {x^2} -x\)

A.  \(\int {f(x) = 2x{e^x} + C}\)

B.  \(\int {f(x) = (2x - 1){e^x} + C}\)

C.  \(\int {f(x) = (2x - 2){e^x} + C}\)

D.  \(\int {f(x) = (2x - 3){e^x} + C}\)

A. \(F(x) = {e^{3x}}\)  

B.  \(F(x) = - \frac{1}{3}{e^{3x}} + \frac{4}{3}\)

C.  \(F(x) = \frac{1}{3}{e^{3x}} + \frac{2}{3}\) 

D. \(F(x) = \frac{1}{3}{e^{3x + 1}}\)

A.  \(\int {f\left( x \right)d{\rm{x}}} = \frac{2}{5}{x^2}\sqrt x + C\)   

B.  \(\int {f\left( x \right)d{\rm{x}}} = \frac{1}{5}{x^2}\sqrt x + C\)

C.  \(\int {f\left( x \right)d{\rm{x}}} = \frac{2}{5}x\sqrt x + C\)

D. \(\int {f\left( x \right)d{\rm{x}}} = \frac{3}{2}\sqrt x + C\)

A.  \(\int {f(x)dx} = - \ln \left| {\cos x} \right| + C\)

B.  \(\int {f(x)dx} = \ln \left| {\cos x} \right| + C\)

C.  \(\int {f(x)dx} = - \ln \left| {\sin x} \right| + C\) 

D.  \(\int {f(x)dx} = \ln \left| {\sin x} \right| + C\)

A.  \(F\left( 1 \right) = 3 - \ln \frac{7}{3}\) 

B.  \(F\left( 1 \right) = 3 + \ln \frac{7}{3}\) 

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

D.  \(F\left( 1 \right) = 3 + \ln 2\)

A.  \(\int {f(x)dx = 2{e^x}(x - 1) - {x^2}}\)

B.  \(\int {f(x)dx = 2{e^x}(x - 1) -4 {x^2}}\)

C.  \(\int {f(x)dx = 2{e^x}(x - 1) -2 {x^2}}\)

D.  \(\int {f(x)dx = 2{e^x}(1-x) - {x^2}}\)

A.  \(\int {f(x)dx = x\sqrt {2 - {x^2}} } + C\)

B.  \(\int {f(x)dx = - \frac{1}{3}({x^2} + 4)\sqrt {2 - {x^2}} } \) \(+ C\)

C.  \(\int {f(x)dx = - \frac{1}{3}{x^2}\sqrt {2 - {x^2}} } + C\)

D.  \(\int {f(x)dx = } - \frac{1}{3}({x^2} - 4)\sqrt {2 - {x^2}} \) \(+ C\)

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

B. \(y = \frac{{{x^4}}}{4} - \frac{{{x^2}}}{2} - 3\)

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

D.  \(y = 3{x^2} - 1\)

A. \(I = \frac{1}{{{e^x} + 1}} + C\)

B. \(I =  - \frac{1}{{{{\left( {{e^x} + 1} \right)}^2}}} + C\)

C. \(I = {e^{ - x + 1}} + C\)

D. \(I = \frac{{{e^x}}}{{{e^x} + 1}} + C\)

A. \(I = \left( {3{x^2} - 7x + 8} \right){e^x} + C\)

B. \(I = \left( {3{x^2} - 7x} \right){e^x} + C\)

C. \(I = \left( {3{x^2} - 7x + 8} \right) + {e^x} + C\)

D. \(I = \left( {3{x^2} - 7x + 3} \right){e^x} + C\)

A. \( - \frac{1}{4}{\rm{cos}}2x + C\)

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

C. \( - \frac{1}{2}{\rm{co}}{{\rm{s}}^2}x + C\)

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

A. \(I = x\tan x + \frac{1}{{{\rm{co}}{{\rm{s}}^2}x}} + \frac{2}{{{\rm{cos}}x}} + C\)

B. \(I = x\tan x + \ln \left| {\cos x} \right| + \frac{2}{{{\rm{cos}}x}} + C\)

C. \(I = x\tan x + \ln \left| {\cos x} \right| - \frac{2}{{{\rm{cos}}x}} + C\)

D. \(I = x\tan x - \frac{1}{{{\rm{co}}{{\rm{s}}^2}x}} - \frac{2}{{{\rm{cos}}x}} + C\)

A. 10 m/s

B. 11 m/s

C. 12 m/s

D. 13 m/s