Đề kiểm tra 1 tiết chương III-Nguyên hàm, tích phân, ứng dụng-Đề 3

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

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

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

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

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

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

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

\({\left( {\int {f(t)dt} } \right)^\prime } = f(t)\).

\(\int\limits_a^b {f(x)dx} - \int\limits_b^c {f(x)dx} = \int\limits_a^c {f(x)dx} \).

\(\int\limits_a^b {f(x)dx} = F\left( a \right) - F(b)\).

\(\int\limits_a^b {f(x)dx} = \int\limits_b^a {f(x)dx} \).

\(\int\limits_a^b {k.f(x)dx} = k\left[ {F\left( b \right) - F(a)} \right]\).

\(\frac{{\pi - 2}}{8}\).

\(\frac{{\pi - 1}}{4}\).

\(3 - \frac{\pi }{2}\).

\(2 - \frac{\pi }{2}\).

\(m.\)

\(mx.\)

\(m + C.\)

\(C.\)

-15

1

20

-1

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

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

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

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

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

\(\ln 2 + 1\).

\(\ln 2\).

\(\frac{1}{2}\).

\(\int\limits_0^1 {2{x^2}dx} = 2\int\limits_0^1 {{x^2}dx} \).

\(\int\limits_0^1 {\frac{{x - 2}}{3}dx} = \frac{1}{3}\int\limits_0^1 {(x - 2)dx} \).

\(\int\limits_0^1 {(2x - 1)dx} = 2\int\limits_0^1 {(x - 1)dx} \)

\(\int\limits_1^2 {x\frac{1}{x}dx} = \int\limits_1^2 {dx} \).

S=\(\left| {\int\limits_a^b {\left[ {f\left( x \right) - g\left( x \right)} \right]} } \right|dx\).

S=\(\int\limits_a^b {\left| {f\left( x \right) - g\left( x \right)} \right|} dx\).

S=\(\int\limits_a^b {\left[ {f\left( x \right) - g\left( x \right)} \right]dx} \).

S=\(\int\limits_a^b {[g\left( x \right) - f(x)]dx} \).

4

\(\frac{{19}}{6}\).

\(\frac{{10}}{3}\).

\(\frac{{16}}{3}\).

0

\(\frac{1}{{12}}\).

-4

\(\frac{1}{6}\).

4

\(\frac{7}{3}\).

\( - \frac{7}{3}\).

\(\frac{5}{3}\).

\( - \frac{1}{5}(\ln \left| {x - 3} \right| - \ln \left| {x + 2} \right|) + C\).

\(\ln \left| {x - 3} \right| - \ln \left| {x + 2} \right| + C\).

\(\ln \left| {{x^2} - x - 6} \right| + C\).

\(\frac{1}{5}(\ln \left| {x - 3} \right| - \ln \left| {x + 2} \right|) + C\).

\(\int {udv = } u.v + \int {vdu} \).

\(\int {udv = } u.v - \int {vdv} \).

\(\int {udv = } u.dv - \int {vdu} \).

\(\int {udv = } u.v - \int {vdu} \).

\(\frac{{2{e^2} + 3}}{3}\).

\(\frac{{3{e^3} + 2}}{8}\).

\(\frac{{2{e^3} + 1}}{9}\).

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

\(I = \frac{2}{3}\).

\(I = \frac{3}{2}\).

\(I = 0\).

\(I = - \frac{2}{3}\).

2

40

-2

\(\frac{{61}}{2}\).

\(F(x) = \frac{1}{3}{\left( {\sqrt {1 + {x^2}} } \right)^2}\).

\(F(x) = \frac{{{x^2}}}{2}{\left( {\sqrt {1 + {x^2}} } \right)^2}\).

\(F(x) = \frac{1}{3}{\left( {\sqrt {1 + {x^2}} } \right)^3}\).

\(F(x) = \frac{1}{2}{\left( {\sqrt {1 + {x^2}} } \right)^2}\).

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

\(\frac{x}{2} + C\).

\(\frac{{{x^2}}}{2}\ln x - \frac{{{x^2}}}{4}\).

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

\(\frac{{{{\sin }^4}x.{{\cos }^3}x}}{{12}} + C\).

\(\frac{{{{\cos }^5}x}}{5} - \frac{{{{\cos }^3}x}}{3} + C\).

\(\frac{{{{\sin }^5}x}}{5} - \frac{{{{\cos }^3}x}}{3} + C\).

\(\frac{{{{\sin }^5}x}}{5} - \frac{{{{\sin }^3}x}}{3} + C\).

\(\int\limits_0^4 {\left[ {f\left( x \right) - g\left( x \right)} \right]} dx = 1.\)

\(\int\limits_0^4 {f\left( x \right)dx} < \int\limits_0^4 {g\left( x \right)} dx.\)

\(\int\limits_0^4 {f\left( x \right)} dx = 5\).

\(\int\limits_0^4 {f\left( x \right)dx} > \int\limits_0^4 {g\left( x \right)} dx.\)

\(\ln 58 - \ln 42\).

\(\ln \frac{{155}}{{12}}\).

\(\ln \frac{{108}}{{15}}\).

\(\ln 77 - \ln 54\).

\(\pi \int\limits_2^5 {\left( {x - 1} \right)dx} \).

\(\int\limits_2^5 {\left( {x - 1} \right)dx} \).

\(\pi \int\limits_2^5 {\sqrt {x - 1} dx} \).

\({\pi ^2}\int\limits_2^5 {\left( {x - 1} \right)dx} \).

9

81

4

3