<![CDATA[一个积分]]>\begin{equation}
-\int r^k \frac{\mathrm{d}}{\mathrm{d}r}\left( \phi ( r ) f( r ) \right) \mathrm{d} r =
\end{equation}
文献里面这么给的
\begin{equation}
-\int r^k \frac{\mathrm{d}}{\mathrm{d}r}\left( \phi ( r ) f( r ) \right) \mathrm{d} r = \int k r^{k-1} \phi ( r ) f ( r ) \mathrm{d} r
\end{equation}
这事我算的：
\begin{equation}
-\int r^k \frac{\mathrm{d}}{\mathrm{d}r}\left( \phi ( r ) f( r ) \right) \mathrm{d} r = -\int r^k \mathrm{d} \left[ \phi( r ) f ( r ) \right]=-\left(r^k \phi( r ) f ( r ) - \int \phi( r ) f ( r ) \mathrm{d} r^k \right)=-r^k \phi( r ) f ( r ) + k \int r^{k-1} \phi( r ) f ( r ) \mathrm{d} r
\end{equation}
后面怎么多出来这个项：$-r^k \phi( r ) f ( r ) $?

]]>https://cfd-china.com/topic/470/一个积分RSS for NodeThu, 12 Mar 2026 10:47:58 GMTThu, 04 Aug 2016 09:54:59 GMT60<![CDATA[Reply to 一个积分 on Tue, 01 Nov 2016 05:28:11 GMT]]>find . -type f | xargs -n 5 touch

]]>https://cfd-china.com/post/2685https://cfd-china.com/post/2685Tue, 01 Nov 2016 05:28:11 GMT<![CDATA[Reply to 一个积分 on Fri, 21 Oct 2016 08:10:03 GMT]]>$\frac{\partial \left( \int v^kn(v)\mathrm{d}d \right)}{\partial v}$ does not equal to $\int v^k\frac{\partial n(v)}{\partial v}\mathrm{d}d$

]]>https://cfd-china.com/post/2600https://cfd-china.com/post/2600Fri, 21 Oct 2016 08:10:03 GMT<![CDATA[Reply to 一个积分 on Fri, 05 Aug 2016 04:47:15 GMT]]>推导的时候忘记了积分限。添加积分限之后则和文献一致。如图：

0_1470372252352_捕获2.JPG

]]>https://cfd-china.com/post/2068https://cfd-china.com/post/2068Fri, 05 Aug 2016 04:47:15 GMT<![CDATA[Reply to 一个积分 on Thu, 04 Aug 2016 14:02:03 GMT]]>0_1470319316675_捕获.PNG

这个是文献里面的。怎么回事呢。

]]>https://cfd-china.com/post/2063https://cfd-china.com/post/2063Thu, 04 Aug 2016 14:02:03 GMT