共50条信息
定积分\(\int_{0}^{1}\dfrac{1}{1{+}x}{dx}\)的值为\((\) \()\)
若\(a=\int_{0}^{2}{{{x}^{2}}dx}\),\(b=\int_{0}^{2}{{{x}^{3}}dx}\),\(c=\int_{0}^{2}{{\sin }xdx}\),则\(a,b,c\)从小到大的顺序为__________.
如图,在边长为\(e(e\)为自然对数的底数\()\)的正方形中随机撒一粒黄豆,则它落到阴影部分的概率为______.
\(∫_{−1}^{1}( \sqrt{1−{x}^{2}}+\sin x)dx =\)_________.
已知\(a > 0\),二项式\(( \dfrac{a}{ \sqrt{x}}-x{)}^{6} \)展开式的常数项为\(15\),则\(∫_{-a}^{a}( \sqrt{1-{x}^{2}}+\sin 2x)dx \)等于__________.
由直线\(y=\dfrac{1}{2},y=2\),曲线\(y=\dfrac{1}{x}\)及\(y\)轴所围成的封闭图形的面积是
计算曲线\(y={{x}^{2}}{-}2x+3\)与直线\(y=x+3\)所围成图形的面积.
函数\(f(x)=\begin{cases}4-x,x\leqslant 0 \\ \sqrt{4-{x}^{2}},0 < x\leqslant 2\end{cases} \),则\(\int_{-2}^{2}{f(x)}dx\)的值为\((\) \()\)
\((1)\)求定积分:\(∫_{0}^{1}\left({e}^{x}+2x\right)dx \)
\((2)\)求函数的导数:\(y\)\(= \dfrac{{x}^{2}+\sin 2x}{{e}^{x}} \)
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