共50条信息
计算\(\int_{1}^{2}{(x+\dfrac{1}{x})dx}\)的值为
一物体在力\(F(x)=4x-1(\)单位：\(N)\)的作用下，沿着与力\(F(x)\)相同的方向从\(x=1\)运动到\(x=3\)处\((\)单位：\(m)\)，则力\(F(x)\)所做的功为 ( )
函数\(f\left( x \right)=\begin{cases} 2-x,{ }x\leqslant 0, \\ \sqrt{4-{{x}^{2}}},0 < x\leqslant 2, \end{cases}\)，则\(\int{_{-2}^{2}}f\left( x \right)dx\)的值为 \((\) \()\)
已知\(n=\int_{_{0}}^{^{2}}x^{3}dx\)，则\(\left( \left. x- \dfrac{2}{ \sqrt[3]{x}} \right. \right)^{n} \)的展开式中常数项为________．
如下图，四边形\(ABCD\)是边长为\(1\)的正方形，\(D\)为\(AD\)的中点，抛物线\(E\)的顶点为\(D\)且通过点\(C\)，则阴影部分的面积为( )
若二项式\({{\left( \dfrac{\sqrt{5}}{5}{{x}^{2}}+\dfrac{1}{x} \right)}^{6}}\)的展开式中的常数项为\(m\)，则\(\int_{1}^{m}{{{x}^{2}}dx}=\)___________．
设\(a=\int _{0}^{1}2xdx \)，则二项式\((ax\)\(2\)\(-\dfrac{1}{x} )\)\(6\)展开式中的常数项为________．
设\(f(x)=\begin{cases} & {{x}^{2}},x\in [0,1], \\ & 2-x,x\in (1,2] \end{cases}\)，则\(\int_{0}^{2}{{}}f(x)dx= \)( )
若\(\int_{1}^{a}{\dfrac{1}{x}}dx=\ln 2,a > 1\)，则\({{\left( x+\dfrac{1}{x} \right)}^{6}}\)的展开式中含\({{x}^{a}}\)的系数是________．
\(\int_{1}^{2}{(x+\dfrac{1}{x})}dx=\)________．
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