3. $\underset{n\to +\infty }{\mathop{\lim }}\,\int_{0}^{1}{\frac{{{x}^{n}}{{e}^{x}}}{1+{{e}^{x}}}dx}=$
A. $0$
B. $e$
C. $\frac{1}{1+e}$
D. $1$
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2. $\underset{n\to +\infty }{\mathop{\lim }}\,\int_{0}^{\frac{1}{2}}{\frac{{{x}^{n}}}{1+{{x}^{2}}}dx}=$
A. $\frac{1}{1+{{x}^{2}}}$
B. $\frac{1}{2}$
C. $1$
D. $0$
1. 定积分$\int_{\frac{\sqrt{3}}{3}}^{\sqrt{3}}{x\arctan xdx}\in $
A. $\left[ 0,\frac{\pi }{9} \right]$
B. $\left[ \frac{2\pi }{3}2\pi \right]$
C. $\left[ \frac{\pi }{9},\frac{2\pi }{3} \right]$
D. $\left[ 2\pi ,4\pi \right]$
8. 下列不等式正确的是
A. $0\lt \int_{0}^{\frac{\pi }{2}}{\sin (\sin x)dx}\lt \int_{0}^{\frac{\pi }{2}}{\cos (\sin x)dx}$
B. $0\lt \int_{0}^{\frac{\pi }{2}}{\cos (\sin x)dx}\lt \int_{0}^{\frac{\pi }{2}}{\sin (\sin x)dx}$
C. $\int_{0}^{\frac{\pi }{2}}{\sin (\sin x)dx}\lt 0\lt \int_{0}^{\frac{\pi }{2}}{\cos (\sin x)dx}$
D. $\int_{0}^{\frac{\pi }{2}}{\cos (\sin x)dx}\lt 0\lt \int_{0}^{\frac{\pi }{2}}{\sin (\sin x)dx}$
7. $\int_{-1}^{1}{{{x}^{2}}\ln (x+\sqrt{1+{{x}^{2}}})}dx=$
A. $1$
B. $-1$
C. $0$
D. 不可积
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