优优班--学霸训练营 > 知识点挑题
全部资源
          排序:
          最新 浏览

          50条信息

            • 1.

              已知\(a > 0\),\({{(\dfrac{a}{\sqrt{x}}-x)}^{6}}\)展开式的常数项为\(15\),则\(\int_{-a}^{a}{({{x}^{2}}+x+\sqrt{4-{{x}^{2}}}})dx=\)      \(\_.\)

            • 2.

              \(\int_{0}^{1}{(\sqrt{1-{{(x-1)}^{2}}}}-2x)dx=\)_______________

            • 3.

              \(∫_{0}^{ \frac{π}{2}}\left(\sin x+a\cos x\right)dx=2 \),则实数\(a\)等于______ .

            • 4. 如图,直线\(y=kx\)分抛物线\(y=x-x^{2}\)与\(x\)轴所围成图形为面积相等的两部分,求\(k\)的值.

            • 5.

              \((1)\)已知\(m= \int_{- \frac{π}{2}}^{ \frac{π}{2}}(\cos x−x+3\sin 2x)dx \),则\({{\left( x-\dfrac{1}{2\sqrt{x}} \right)}^{3m}}\)的展开式中,常数项为_________


              \((2)\int_{-1}^{1}{(\sqrt{1-{{x}^{2}}}}-1)dx=\)________.


              \((3)\)设\(n\)为正整数,\(f\left( n \right)=1+\dfrac{1}{2}+\dfrac{1}{3}+\ldots +\dfrac{1}{n}\),计算得\(f\left( 2 \right)=\dfrac{3}{2}\),\(f\left( 4 \right) > 2\),\(f\left( 8 \right) > \dfrac{5}{2}\),\(f\left( 16 \right) > 3\),观察上述结果,按照上面规律,可推测\(f\left( 4096 \right) > \)_____.


              \((4)\)若复数\(z=(x+i)(1+i)\)是纯虚数,其中\(x\)为实数,\(i\)为虚数单位,则\(z\)的共轭复数\(\overline{z}=\)______.

            • 6.
              定积分\( \int _{ 0 }^{ 1 }(2x+e^{x})dx\)的值为\((\)  \()\)
              A.\(e+2\)
              B.\(e+1\)
              C.\(e\)
              D.\(e-1\)
            • 7.

              已知\(f(a)=\int_{0}^{1}{(3{{a}^{3}}{{x}^{2}}-{{a}^{2}}x)}dx,(0\leqslant a\leqslant 2)\)则函数\(f(a)\)的最大值为________.

            • 8.

              \(∫_{0}^{2}\left(2-\left|1-x\right|\right)dx= \)          

            • 9.

              按要求进行计算。

              求导数:

              \((1)y={{(2{{x}^{3}}-x+\dfrac{1}{x})}^{4}}\)                  \((2)y=\ln \sqrt{{{x}^{2}}+1}\)


              求定积分:

              \((3)\int _{0}^{ \frac{π}{2}}(2{\cos }^{2} \dfrac{x}{2}+1)dx \)                  \((4)\int_{1}^{2}{\sqrt{4-{{x}^{2}}}}dx\)

            • 10.

              \(∫_{−1}^{1}({x}^{2}−1)dx= \)                              

            0/40

            进入组卷