共50条信息
已知函数\(f\left( x \right)={f}{{{"}}}\left( 1 \right){{x}^{2}}+x+2\)，则\(\int_{0}^{1}{f\left( x \right)dx=}\)( )
\(\int{_{-1}^{1}}(x\cos x+\sqrt[3]{{{x}^{2}}})dx\)的值为 ( )
设\(f(x)=\begin{cases} x^{2},x∈[0,1], \\ \dfrac{1}{x},x∈(1,e], \end{cases}\)则\(\int_{0}^{e}{f\left( x \right){dx}}\)等于\((\) \()\)
定积分\(\int_{0}^{1}{({{{e}}^{x}}+2x){d}x}\)的值为\((\) \()\)
已知数列\(\left\{ {{a}_{n}} \right\}\)为等差数列，且\({{a}_{2016}}+{{a}_{2018}}=\int_{0}^{2}{\sqrt{4-{{x}^{2}}}}dx\)，则\({{a}_{2017}}\)的值为( )
利用定积分的性质求\(∫_{-1}^{1}\left( \dfrac{2x}{{x}^{4}+1}+{\sin }^{3}x+{x}^{2}- \dfrac{{e}^{x}-1}{{e}^{x}+1}\right)dx \)
若等比数列\(\left\{{a}_{n}\right\} \)的首项为\(\dfrac{2}{3}\)，且\({{a}_{4}}=\int_{_{{}}1}^{^{{}}4}{(1+2x)dx}\)，则公比等于\((\) \()\)
已知函数\(f(x)=x^{2}-x+2\)，则\(∫_{0}^{1}f(x)dx= (\) \()\)
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