\(已知L是抛物线y=x^2上点O(0,0)与点A(1,1)之间的一段弧,则\int_{L}\sqrt{y}ds=(\,)\)
A: \[\frac{1}{12}(5\sqrt{5}-1)\]
B: \[\frac{1}{12}(3\sqrt{3}-1)\]
C: \[\frac{1}{13}(5\sqrt{5}-1)\]
D: \[\frac{1}{13}(3\sqrt{3}-1)\]
A: \[\frac{1}{12}(5\sqrt{5}-1)\]
B: \[\frac{1}{12}(3\sqrt{3}-1)\]
C: \[\frac{1}{13}(5\sqrt{5}-1)\]
D: \[\frac{1}{13}(3\sqrt{3}-1)\]
举一反三
- 计算\(\int_L {\sqrt y } ds\),其中\(L\)是抛物线\(y=x^2\)上点\((0,0)\)与\((1,1)\)之间的一段弧。 A: \({1 \over {12}}(6\sqrt 5 - 1)\) B: \({1 \over {12}}(5\sqrt 6 - 1)\) C: \({1 \over {12}}(5\sqrt 5 - 1)\) D: \({1 \over {12}}(5\sqrt 5 + 1)\)
- \(已知曲线弧L:y=\sqrt{1-x^2}(0\le x\le 1).则\int_{L}xyds=(\,)\) A: \[1\] B: \[\frac{1}{2}\] C: \[\frac{1}{3}\] D: \[\frac{1}{4}\]
- 设随机变量服从区间(0,2)上的均匀分布,则$Y=X^{2}$在(0,4)上的密度函数为() A: $\frac{1}{3\sqrt{y}}$ B: $\frac{1}{\sqrt{y}}$ C: $\frac{1}{2\sqrt{y}}$ D: $\frac{1}{4\sqrt{y}}$
- \(已知L为抛物线y^2=x上从点A(1,-1)到点B(1,1)的一段弧,则\int_{L}xyds=(\,)\) A: \[\frac{4}{5}\] B: \[\frac{3}{5}\] C: \[\frac{2}{5}\] D: \[\frac{1}{5}\]
- 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: $\sqrt{2}+\frac{1}{\sqrt{2}}(y-1)$