Bộ 15 đề thi giữa kì 2 Toán 12 có đáp án năm 2022-2023 (Đề 2)

Nếu $\int f\left(x\right)\text{\hspace{0.17em}d}x=F\left(x\right)+C$ thì $\int f\left(u\right)\text{\hspace{0.17em}d}u=F\left(u\right)+C.$

$\int kf\left(x\right)\text{\hspace{0.17em}d}x=k\int f\left(x\right)\text{\hspace{0.17em}d}x$ (k là hằng số và $k\ne 0$).

Nếu F(x) và G(x) đều là nguyên hàm của hàm số f(x) thì $F\left(x\right)=G\left(x\right).$

$\int \left[f\left(x\right)+g\left(x\right)\right]\text{\hspace{0.17em}d}x=\int f\left(x\right)\text{\hspace{0.17em}d}x+\int g\left(x\right)\text{\hspace{0.17em}d}x.$

$\frac{x^4}{4}+x^3+x+C.$

$x^4+x^3+x+C.$

$\frac{x^4}{4}+2x^3+x^2+C.$

$\frac{x^4}{4}+3x^3+2x+C.$

$\cos x+C$.

$-\cos x+C$.

$-\sin x+C$.

$\sin x+C$.

$\ln \left|x+1\right|+C$.

$2\ln \left|x+1\right|+C$.

$\frac{1}{2}\ln \left|x+1\right|+C$.

$\ln \left|x\right|+C$.

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

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

$F\left(x\right)=e^x+x^2+\frac{5}{2}$.

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

$\int \alpha .f\left(x\right)\text{d}x=\alpha \int f\left(x\right)\text{d}x$.

$\int f\left(x\right)g\left(x\right)\text{d}x=\int f\left(x\right)\text{d}x.\int g\left(x\right)\text{d}x$.

$\int \left[f\left(x\right)\text{+}g\left(x\right)\right]\text{d}x=\int f\left(x\right)\text{d}x+\int g\left(x\right)\text{d}x$.

$\int \left[f\left(x\right)-g\left(x\right)\right]\text{d}x=\int f\left(x\right)\text{d}x+\int g\left(x\right)\text{d}x$.

$F\left(-5x+1\right)+C$.

$-\frac{1}{5}F\left(-5x+1\right)+C$.

$-5F\left(-5x+1\right)+C$.

$\frac{1}{5}F\left(x\right)+C$.

$\underset{a}{\overset{b}{\int }}f\left(x\right)\text{d}x=f\left(b\right)-f\left(a\right)$.

$\underset{a}{\overset{b}{\int }}f\left(x\right)\text{d}x=f\left(a\right)-f\left(b\right)$.

$\underset{a}{\overset{b}{\int }}f\left(x\right)\text{d}x=F\left(b\right)-F\left(a\right)$.

$\underset{a}{\overset{b}{\int }}f\left(x\right)\text{d}x=F\left(a\right)-F\left(b\right)$.

$-\frac{1}{2}$.

$\frac{3}{4}$.

ln 3.

ln 2.

$V=\pi \underset{a}{\overset{b}{\int }}{f}^2\left(x\right)\text{d}x$

$V=\underset{a}{\overset{b}{\int }}{f}^2\left(x\right)\text{d}x$

$V={\pi }^{}\underset{a}{\overset{b}{\int }}\left|f\left(x\right)\right|\text{d}x$

$V={\pi }^2\underset{a}{\overset{b}{\int }}{f}^2\left(x\right)\text{d}x$

-4.

8.

4.

-8.

$\underset{a}{\overset{b}{\int }}\left(f\left(x\right)+g\left(x\right)\right)\text{\hspace{0.17em}d}x=\underset{b}{\overset{a}{\int }}f\left(x\right)\text{\hspace{0.17em}d}x+\underset{a}{\overset{b}{\int }}g\left(x\right)\text{d}x$.

$\underset{a}{\overset{b}{\int }}\left(f\left(x\right)+g\left(x\right)\right)\text{\hspace{0.17em}d}x=\underset{a}{\overset{b}{\int }}f\left(x\right)\text{\hspace{0.17em}d}x-\underset{a}{\overset{b}{\int }}g\left(x\right)\text{\hspace{0.17em}d}x$.

$\underset{a}{\overset{b}{\int }}\left(f\left(x\right)+g\left(x\right)\right)\text{\hspace{0.17em}d}x=\underset{a}{\overset{b}{\int }}f\left(x\right)\text{\hspace{0.17em}d}x+\underset{b}{\overset{a}{\int }}g\left(x\right)\text{d}x$.

$\underset{a}{\overset{b}{\int }}\left(f\left(x\right)+g\left(x\right)\right)\text{\hspace{0.17em}d}x=\underset{a}{\overset{b}{\int }}f\left(x\right)\text{\hspace{0.17em}d}x-\underset{b}{\overset{a}{\int }}g\left(x\right)\text{d}x$.

$-\frac{2}{5}$.

5.

10.

-10.

2.

1.

8.

-8.

$\left(1;3;2\right)$.

$\left(-1;2;-3\right)$.

$\left(-1;3;2\right)$.

$\left(1;2;3\right)$.

$Q\left(0;2;-3\right)$.

$P\left(1;2;0\right)$.

$N\left(1;0;-3\right)$.

$M\left(0;2;0\right)$.

$I\left(1;-2;-2\right)$ và $R=8$.

$I\left(-1;2;2\right)$ và $R=\sqrt{7}$.

$I\left(1;-2;-2\right)$ và $R=4$.

$I\left(1;-2;-2\right)$ và $R=\sqrt{2}$.

$2x-y+3z-4=0$.

$x-2y-4=0$.

$2x-y+3z+4=0$.

$2x-y+3z+9=0$.

$\left(P\right):x-y+2z-2=0$.

$\left(R\right):x+y-2z+1=0$.

$\left(Q\right):x+y-2z-2=0$.

$\left(S\right):x+y+2z-1=0$.

$\frac{x}{1}+\frac{y}{3}+\frac{z}{-2}=1$.

$\frac{x}{1}+\frac{y}{3}+\frac{z}{2}=-1$.

$\frac{x}{1}+\frac{y}{3}+\frac{z}{-2}=-1$.

$\frac{x}{1}+\frac{y}{3}+\frac{z}{2}=1$.

$2\sin 2x+C$.

$-\sin 2x+C$.

$\frac{-1}{2}\sin 2x+C$.

$\frac{1}{2}\sin 2x+C$.

1.

$\frac{1}{2}$.

$\frac{3}{2}$.

$\frac{4}{3}$.

$-\sin x-2+C$.

$-\sin x-x^2+C$.

$\sin x-2x^2+C$.

$\sin x-x^2+C$.

$\frac{x^2}{2}-x+\frac{2}{x}+C$.

$\frac{x^2}{2}-x-\frac{2}{x}+C$.

$\frac{x^2}{2}-x+\frac{2}{3x^3}+C$.

$\frac{x^2}{2}-x+\frac{2}{x^3}+C$.

$\int 2x\ln \left(x-1\right)\text{\hspace{0.17em}d}x=x^2\ln \left(x-1\right)-\int \left(x+1\right)\text{\hspace{0.17em}d}x$.

$\int 2x\ln \left(x-1\right)\text{\hspace{0.17em}d}x=x\ln \left(x-1\right)-\int \left(x-1\right)\text{\hspace{0.17em}d}x$.

$\int 2x\ln \left(x-1\right)\text{\hspace{0.17em}d}x=\left(x^2-1\right)\ln \left(x-1\right)+\int \left(x+1\right)\text{\hspace{0.17em}d}x$.

$\int 2x\ln \left(x-1\right)\text{\hspace{0.17em}d}x=\left(x^2-1\right)\ln \left(x-1\right)-\int \left(x+1\right)\text{\hspace{0.17em}d}x$.

$I=-7$.

$I=4$.

$I=3$.

$I=7$.

$I=\frac{1}{{\text{e}}^2}+\frac{3}{\text{e}}$.

$I=1-\frac{1}{\text{e}}-{\text{e}}^2$.

$I=\frac{1}{{\text{e}}^2}-\frac{3}{\text{e}}$.

$I=1-\frac{3}{\text{e}}$.

-4.

1.

8.

4.

15.

0.

6.

-15.

1.

$\frac{1}{2}$.

2.

4.

$a+b=1$.

$a^2+b^2=8$

$a-b=2$.

$ab=-3$.

45.

42.

44.

43.

${\left(x+3\right)}^2+{\left(y-3\right)}^2+{\left(z-1\right)}^2=26$.

${\left(x-3\right)}^2+{\left(y+3\right)}^2+{\left(z+1\right)}^2=26$.

${\left(x+3\right)}^2+{\left(y-3\right)}^2+{\left(z-1\right)}^2=52$.

${\left(x-3\right)}^2+{\left(y+3\right)}^2+{\left(z+1\right)}^2=52$.

$2x+2y-3z+9=0$.

$2x-2y+3z+9=0$.

$4x-4y-6z+9=0$.

$2x-2y+3z-9=0$.

4.

6.

$\frac{2}{3}$.

2.