Commit 417f6c1b authored by Claude Meny's avatar Claude Meny

Update cheatsheet.fr.md

parent 6832b711
Pipeline #18230 canceled with stage
......@@ -777,16 +777,18 @@ figure à faire
$`\color{blue}{\scriptsize{\text{étant } n\cdot u^{n-1}\cdot u'\;\text{, alors}}}`$
$`\color{blue}{\scriptsize{\text{la primitive de } n\cdot u^{n-1}\cdot u' \text{ est } u^n}}`$
$`\color{blue}{\scriptsize{\text{soit encore }}}`$
$`\color{blue}{\scriptsize{\text{la primitive de } u'\cdot u^n \text{ est } \dfrac{1}{n+1}\,u^{n+1}}}`$
$`\color{blue}{\scriptsize{\text{la primitive de } (n+1)\cdot u^n \cdot u' \text{ est } u^{n+1}}`$
*$`\mathbf{\boldsymbol{E_M}}`$*
$`\displaystyle\;=\dfrac{\dens^{2D}\,z_M}{2\,\epsilon_0}
\times
\int_{\rho=0}^{R} \rho\,(\rho^2+z_M^2)^{\,-3/2}\,d\rho`$
<br>
$`\displaystyle \hspace{1cm} = \dfrac{\dens^{2D}\,z}{2\epsilon_0} \int_{\rho = 0}^R\dfrac{1}{2}\times
$`\displaystyle \hspace{1cm} = \dfrac{\dens^{2D}\,z}{2\epsilon_0} \int_{\rho = 0}^R-\Big\underbrace{(-\dfrac{1}{2}\Big)}_{n+1}\times
\underbrace{2\rho}_{u^{\,'}}\,\underbrace{(\rho^2+z^2)^{-\,3/2}}_{u^n}\,d\rho`$
<br>
$`\color{blue}{\scriptsize{\text{le signe moins devant } (n+1)\cdot u^n \cdot u' \text{ devient un plus en inversant les bornes d'intégration}`$
<br>
$`\displaystyle \hspace{1cm} = \dfrac{\dens^{2D}\,z}{2\epsilon_0} \big[\underbrace{\dfrac{1}{2}\times\dfrac{1}{-3/2+1}}
_{=\frac{1}{2}\,\times \,(-2) \,=\, -1}(\rho^2+z^2)^{-\,1/2}\big]_0^R`$
<br>
......
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