大家好,又见面了,我是你们的朋友全栈君。
\(L\)为\(R^{3}\)中的可求导的长曲线,函数\(f(x,y,z)\)在\(L\)上有定义 习题: \(\int\limits_{L}|x|^{\frac{1}{3}}ds\)(\(L\):星形线\(x^{\frac{2}{3}} +y^{\frac{2}{3}} = a^{\frac{2}{3}}\))
设S为可求面积的曲面函数,\(f(x,y,z)\)在\(S\)上面有定义,将其分割为\(S_{1},S_{2},S_{3},\dots,S_{n}\) 在每个小块曲面上\(S_{j}\)任取一点\(Q_{j}=(\xi_{j},\eta_{j},\zeta_{j})\)
\(\int_\limits{\alpha D}Pdx+Qdy=\iint_\limits{D} (\frac{\alpha Q}{\alpha x}-\frac{\alpha P}{\alpha y})dxdy\)
\(\iiint_{\Omega} (\frac{\alpha P}{\alpha x}+\frac{\alpha Q}{\alpha y}+\frac{\alpha R}{\alpha z})dxdydz\)
\(\int_\limits{\sum}Pdx+Qdy+Rdz=\iint_\limits{\sum}\) \(\begin{vmatrix} dydz & dzdx & dxdy \\ \frac{\alpha}{\alpha x} & \frac{\alpha}{\alpha y} & \frac{\alpha}{\alpha z} \\ P & Q & R \end{vmatrix} \quad\)
发布者:全栈程序员栈长,转载请注明出处:https://javaforall.cn/168208.html原文链接:https://javaforall.cn