70 câu trắc nghiệm Toán 12 Chân trời sáng tạo Bài 1. Nguyên hàm có đáp án - Đề 1

A. \[\int {f(x)dx = } F(x) + C\].

B. \({\left( {\int {f(x)dx} } \right)^\prime } = f(x)\).

C. \({\left( {\int {f(x)dx} } \right)^\prime } = f'(x)\).

D. \({\left( {\int {f(x)dx} } \right)^\prime } = F'(x)\).

A. \[{x^2} + C\].

B. \[{x^2} + 6x + C\].

C. \[2{x^2} + C\].

D. \[2{x^2} + 6x + C\].

A. \(2x + C\).

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

C. \({x^3} + C\).

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

A. \({x^3} + C\)

B. \(\frac{{{x^3}}}{3} + x + C\)

C. \(6x + C\)

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

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

B. \(3{x^2} + 1 + C\)

C. \({x^3} + x + C\)

D. \({x^4} + {x^2} + C\)

A. \[\frac{1}{5}{x^5} + \frac{1}{3}{x^3} + C\]

B. \[{x^4} + {x^2} + C\]

C. \[{x^5} + {x^3} + C\].

D. \[4{x^3} + 2x + C\]

A. \(\frac{{{x^{2023}}}}{{2023}} + 1\).

B. \(\frac{{{x^{2023}}}}{{2023}}\).

C. \(y = 2022{x^{2021}}\).

D. \(\frac{{{x^{2023}}}}{{2023}} - 1\).

A. \[\frac{1}{{12}}{x^4} - \frac{2}{3}{x^3} + \frac{{{x^2}}}{2} + C\].

B. \(\frac{1}{9}{x^4} - \frac{2}{3}{x^3} + \frac{{{x^2}}}{2} - 2024x + C\).

C. \(\frac{1}{{12}}{x^4} - \frac{2}{3}{x^3} + \frac{{{x^2}}}{2} - 2024x + C\).

D. \(\frac{1}{9}{x^4} + \frac{2}{3}{x^3} - \frac{{{x^2}}}{2} - 2024x + C\).

A. \[F\left( x \right)\, = \,\frac{{{x^4}}}{4}\, - \,6{x^3}\, + \,\frac{{11}}{2}{x^2} - \,6x\, + \,C\].B. \[F\left( x \right)\, = \,{x^4}\, + \,6{x^3}\, + \,11{x^2} + \,6x\, + \,C\].

C. \[F\left( x \right)\, = \,\frac{{{x^4}}}{4}\, + 2{x^3}\, + \,\frac{{11}}{2}{x^2} + \,6x\, + \,C\].D. \[F\left( x \right)\, = \,{x^3}\, + \,6{x^2}\, + \,11{x^2} + \,6x\, + \,C\].

A. \(\int {f\left( x \right){\rm{d}}x} = \frac{{{x^3}}}{3} + \frac{1}{x} + C\).

B. \(\int {f\left( x \right){\rm{d}}x} = \frac{{{x^3}}}{3} - \frac{2}{x} + C\).

C. \(\int {f\left( x \right){\rm{d}}x} = \frac{{{x^3}}}{3} - \frac{1}{x} + C\).

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

A. \(\frac{4}{{15}}x\sqrt[{15}]{{{x^7}}} + C\).

B. \(\frac{8}{{15}}x\sqrt[{15}]{{{x^7}}} + C\).

C. \(\frac{8}{{15}}x\sqrt[{15}]{x} + C\).

D. \(\frac{4}{{15}}x\sqrt[{15}]{x} + C\).

A. \[x\sqrt[5]{x} - 2x\sqrt[{17}]{{{x^5}}} + \sqrt[4]{{{x^3}}} + C\].

B. \[\frac{4}{5}x\sqrt[5]{x} - \frac{{24}}{{17}}x\sqrt[{17}]{{{x^5}}} + \frac{4}{3}\sqrt[4]{{{x^3}}} + C\].

C. \[x\sqrt[5]{x} - \frac{{24}}{{17}}x\sqrt[{17}]{{{x^5}}} + \sqrt[4]{{{x^3}}} + C\].

D. \[\frac{4}{5}x\sqrt[5]{x} - 2x\sqrt[{17}]{{{x^5}}} + \frac{4}{3}\sqrt[4]{{{x^3}}} + C\].

A. \(\int f (x)dx = 2x + C\).

B. \(\int f (x)dx = {x^2} + 4x + C\).

C. \(\int f (x)dx = \frac{{{x^3}}}{3} + 4x + C\).

D. \(\int f (x)dx = {x^3} + 4x + C\).

A. \(\int {f\left( x \right)} dx = \frac{3}{2}{x^{\frac{1}{2}}} + C\).

B. \(\int {f\left( x \right)} dx = \int {\sqrt {{x^3}} } dx\).

C. \(\int {f\left( x \right)} dx = \frac{2}{5}{x^{\frac{5}{2}}} + C\).

D. \(\int {f\left( x \right)} dx = \frac{2}{3}{x^{\frac{1}{2}}} + C\).

A. \(\int {f\left( x \right){\rm{d}}x = } \frac{{{x^3}}}{3} - \frac{1}{x} + C\).

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

C. \[\int {f\left( x \right){\rm{d}}x = } \int {\left( {{x^2} + \frac{2}{{{x^2}}}} \right)} {\rm{d}}x\].

A. \(f\left( x \right) = 6{x^2} - 2\)

B. \(f\left( x \right) = \frac{1}{2}{x^4} - {x^2} + x\)

C. \(f\left( x \right) = \frac{1}{2}{x^4} - {x^2} + x + C\).

D. \(f\left( x \right) = 6{x^2} - 2 + C\).

A. \(\int {F'\left( x \right)dx = F\left( x \right) + C} \).

B. \(\int {F\left( x \right)dx = F'\left( x \right) + C} \).

C. \(\int {F\left( x \right)dx = F\left( x \right) + C} \).

D.\(\int {F'\left( x \right)dx = F'\left( x \right) + C} \).

A. \[\int {{e^{ - 3x}}dx} = {e^{ - 3x}} + C\].

B. \[\int {{e^{ - 3x}}dx} = - \frac{1}{3}{e^{ - 3x}} + C\].

C. \[\int {{e^{ - 3x}}dx} = \frac{1}{3}{e^{ - 3x}} + C\].

D.\[\int {{e^{ - 3x}}dx} = - \frac{1}{3}{e^{ - 3x}}\].

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

B. \[\frac{{{2^{\sqrt 2 }}{x^{\sqrt 2 + 1}}}}{{\sqrt 2 + 1}} + C\].

C. \[\frac{{{{\left( {2x} \right)}^{\sqrt 2 }}}}{{\ln \left( {2x} \right)}} + C\].

D. \[{\left( {2x} \right)^{\sqrt 2 }} + C\].

A. \[x - \cos x + C\].

B. \[{\left( { - \cos \frac{x}{2} + \sin \frac{x}{2}} \right)^2} + C\].

C. \[\frac{1}{3}{\left( {\sin \frac{x}{2} + \cos \frac{x}{2}} \right)^3} + C\].

D. \[x + \cos x + C\].

A. \({f_2}\left( x \right) = \frac{1}{{{{\sin }^2}x}}\).

B. \({f_1}\left( x \right) = - \frac{1}{{{{\cos }^2}x}}\).

C. \({f_4}\left( x \right) = \frac{1}{{{{\cos }^2}x}}\).

D. \({f_3}\left( x \right) = - \frac{1}{{{{\sin }^2}x}}\).

A. \(\int {f\left( x \right){\rm{d}}x} = x - \cos x + C\).

B. \(\int {f\left( x \right){\rm{d}}x} = x + \sin x + C\).

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

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

B. A. \(F\left( x \right) = 2\cos \frac{x}{2} + C\)

C. B. \(F\left( x \right) = \frac{1}{2}\left( {1 + \sin x} \right) + C\)

D. C. \(F\left( x \right) = 2\sin \frac{x}{2} + C\)

A. D. \(F\left( x \right) = \frac{1}{2}\left( {1 - \sin x} \right) + C\)

A. \(\int {f\left( x \right){\rm{d}}x} = x + \tan x + C\).

B. \(\int {f\left( x \right){\rm{d}}x} = x + \cot x + C\).

C. \(\int {f\left( x \right){\rm{d}}x} = x - \tan x + C\).

D. \(\int {f\left( x \right){\rm{d}}x} = x - \cot x + C\).

A. \(\sin x + 3{x^2} + C\).

B. \( - \sin x + 3{x^2} + C\).

C. \(\sin x + 6{x^2} + C\).

D. \( - \sin x + C\).

A. \(\int {\left( {2\sin x + 3x} \right)dx = - 2\cos x + \frac{3}{2}{x^2} + C} \)

B. \(\int {\left( {2\sin x + 3x} \right)dx = 2\cos x + 3{x^2} + C} \)

C. \(\int {\left( {2\sin x + 3x} \right)dx = {{\sin }^2}x + \frac{3}{2}x + C} \)

D. \(\int {\left( {2\sin x + 3x} \right)dx = \sin 2x + \frac{3}{2}{x^2} + C} \)

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

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

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

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

A. \[{x^3} + \cos x + C\].

B. \[6x + \cos x + C\].

C. \[{x^3} - \cos x + C\].

D. \[6x - \cos x + C\].

A. \(\ln x - \cos x + C\).

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

C. \(\ln \left| x \right| + \cos x + C\).

D. \(\ln \left| x \right| - \cos x + C\).

A. \(f\left( x \right) = - \sin x\).

B. \(f\left( x \right) = - \cos x\).

C. \(f\left( x \right) = \sin x\).

D. \(f\left( x \right) = \cos x\).