共50条信息
已知\(a=\dfrac{1}{\pi }\underset{2}{\overset{-2}{\int}}\,\left( \sqrt{4-{{x}^{2}}}+{\sin }x \right)dx\)，则二项式\({{\left( \dfrac{x}{2}-\dfrac{a}{{{x}^{2}}} \right)}^{9}}\)的展开式中的常数项为 \((\) \()\)
如图，设点\(P\)从原点沿曲线\(y=x\)\({\,\!}^{2}\)向点\(A(2,4)\)移动，直线\(OP\)与曲线\(y=x\)\({\,\!}^{2}\)围成图形的面积为\(S\)\({\,\!}_{1}\)，直线\(OP\)与曲线\(y=x\)\({\,\!}^{2}\)及直线\(x=2\)围成图形的面积为\(S\)\({\,\!}_{2}\)，若\(S\)\({\,\!}_{1}\)\(=S\)\({\,\!}_{2}\)，求点\(P\)的坐标．
已知等差数列\(\{a_{n}\}\)中，\(a_{5}+a_{7}=\int _{0}^{π}\sin xdx \)，则\(a_{4}+a_{6}+a_{8}=(\) \()\)
若\({{\left( {{x}^{{2}}}-\dfrac{{1}}{ax} \right)}^{{9}}}(a\in R)\)展开式中\(x^{9}\)的系数是\(-\dfrac{{21}}{{2}}\)，则\(\int_{0}^{a}{\sin xdx}\)等于 \((\) \()\)
\(F(x)=\int _{0}^{x}({t}^{2}+2t-8)dt (x > 0)\)．
\((1)\)求\(F(x)\)的单调区间．
\((2)\)求函数\(F(x)\)在\([1,3]\)上的最值．
\(∫_{0}^{2}\left(3{x}^{2}+k\right)dx=10,则k= \) ________\(.\)
已知\(m=3\int_{0}^{\pi }{\sin xdx}\)，则二项式\({{(a+2b-3c)}^{m}}\)的展开式中\(a{{b}^{2}}{{c}^{m-3}}\)的系数为________．
若\(a{=}\int_{\frac{\pi}{2}}^{2}\sin{xdx}{,}b{=}\int_{0}^{1}\cos{xdx}\)，则\(a\)与\(b\)的关系是\(({ })\)
计算\(\int_{-1}^{1}{(\sqrt{1-{{x}^{2}}}+{{e}^{|x|}})}dx=\)______________．
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