单选题 （共 6 题 ），每题只有一个选项正确
设 $I_k=\int_0^{k \pi} e^{x^2} \sin x \mathrm{~d} x(k=1,2,3)$ ，则有
$\text{A.}$ $I_1 < I_2 < I_3$
$\text{B.}$ $I_3 < I_2 < I_1$
$\text{C.}$ $I_2 < I_3 < I_1$
$\text{D.}$ $I_2 < I_1 < I_3$
设 $$
\begin{aligned}
M & =\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \frac{(1+x)^2}{1+x^2} \mathrm{~d} x, \\
N & =\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \frac{1+x}{e^x} \mathrm{~d} x \\
K &=\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}(1+\sqrt{\cos x}) \mathrm{d} x ，
\end{aligned}
$$
则 $M, N, K$ 的大小关系为
$\text{A.}$ $M>N>K$
$\text{B.}$ $M>K>N$
$\text{C.}$ $K>M>N$
$\text{D.}$ $K>N>M$
记 $I=\int_0^1 \frac{\sin x}{x} \mathrm{~d} x, J=\int_0^1 \frac{\tan x}{x} \mathrm{~d} x$, 则
$\text{A.}$ $\sin 1>I$
$\text{B.}$ $I>1$
$\text{C.}$ $J < \tan 1$
$\text{D.}$ $J < 1$
设 $I_1=\int_0^\pi \mathrm{e}^{-x^2} \cos x \mathrm{~d} x, I_2=\int_{\frac{\pi}{2}}^{\frac{3 \pi}{2}} \mathrm{e}^{-x^2} \cos x \mathrm{~d} x, I_3=\int_\pi^{2 \pi} \mathrm{e}^{-x^2} \cos x \mathrm{~d} x$, 则
$\text{A.}$ $I_1 < I_2 < I_3$.
$\text{B.}$ $I_3 < I_2 < I_1$.
$\text{C.}$ $I_2 < I_3 < I_1$.
$\text{D.}$ $I_2 < I_1 < I_3$.
$I_1=\int_0^1 \frac{x}{2(1+\cos x)} d x, I_2=\int_0^1 \frac{\ln 1+x}{1+\cos x} d x, I_3=\int_0^1 \frac{2 x}{1+\sin x} d x$, 则
$\text{A.}$ $I_1 < I_2 < I_3$
$\text{B.}$ $I_2 < I_3 < I_1$
$\text{C.}$ $I_1 < I_3 < I_2$
$\text{D.}$ $I_2 < I_1 < I_3$
设 $I_1=\int_0^{\frac{\pi}{2}} \sin (\sin x) \mathrm{d} x, I_2=\int_0^{\frac{\pi}{2}} \cos (\sin x) \mathrm{d} x$, 则
$\text{A.}$ $I_1 < 1 < I_2$.
$\text{B.}$ $1 < I_1 < I_2$.
$\text{C.}$ $I_2 < 1 < I_1$.
$\text{D.}$ $I_1 < I_2 < 1$.