\(\int_{-\sqrt{2}}^{\sqrt{2}}{\sqrt{8-2 { { y}^{2}}}dy}\)=( )。
A: \(\sqrt{2}(\pi -2)\)
B: \(\sqrt{2}(\pi +2)\)
C: \(2\sqrt{2}(\pi +2)\)
D: \(2\sqrt{2}(\pi -2)\)
A: \(\sqrt{2}(\pi -2)\)
B: \(\sqrt{2}(\pi +2)\)
C: \(2\sqrt{2}(\pi +2)\)
D: \(2\sqrt{2}(\pi -2)\)
举一反三
- \( \int_0^1 {dx} \int_ { { x^2}}^x { { {\left( { { x^2} + {y^2}} \right)}^{ - {1 \over 2}}}dy} \) =（ ） A: \( \sqrt 2 + 1 \) B: \( \sqrt 2 - 1 \) C: \( \sqrt 2 \) D: \( \pi \)
- Solve $\int_{-\frac{1}{2}}^1{1-x^2}dx=$? A: $\frac{\pi}{3}+\frac{\sqrt{3}}{8}$. B: $\frac{\pi}{2}$. C: $\frac{\pi}{6}+\frac{\sqrt{3}}{4}$. D: $\frac{\pi}{4}$.
- 函数$f(x,y)=\sqrt{1+{{y}^{2}}}\cos x$在点$(0,1)$处的1次Taylor多项式为 A: $\sqrt{2}-\frac{1}{\sqrt{2}}(y-1)$ B: $\frac{\sqrt{2}}{2}+\frac{1}{\sqrt{2}(}y-1)$ C: $2\sqrt{2}+\frac{1}{\sqrt{2}}(y-1)$ D: $\sqrt{2}+\frac{1}{\sqrt{2}}(y-1)$
- $\int_{0}^{\frac{\text{ }\!\!\pi\!\!\text{ }}{4}}{[\cos (2t)\mathbf{i}+\sin (2t)\mathbf{j}+t\sin t\mathbf{k}]}\operatorname{dt}=$( ) A: $(\frac{1}{2},\frac{1}{2},\frac{4-\text{ }\!\!\pi\!\!\text{ }}{4\sqrt{2}})$ B: $(1,\frac{1}{2},\frac{4-\text{ }\!\!\pi\!\!\text{ }}{4\sqrt{2}})$ C: $(\frac{1}{2},1,\frac{4-\text{ }\!\!\pi\!\!\text{ }}{4\sqrt{2}})$ D: $(1,1,\frac{4-\text{ }\!\!\pi\!\!\text{ }}{4\sqrt{2}})$
- 曲线\(y = \ln x\) 在点\((1,0)\)处的曲率为 （ ）。 A: \(2\sqrt 2 \) B: \(\sqrt 2 \) C: \( { { \sqrt 2 } \over 2}\) D: \( { { \sqrt 2 } \over 4}\)