from github to this gitea

Exercices maths perso 2022-10-08.md

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+#exercice #maths
+
+----
+![800](app://local/Users/oscarplaisant/devoirs/cours/attachments/markmind/1664963348304.png?1664963348339)
+
+$\displaystyle I_{4} = \int_{0}^{\frac{\pi}{2}} \frac{\sin ^{3}t}{1+\cos ^{2}t} \, dt$
+
+On pose $x = \cos t$, alors $t = \arccos x$
+
+$\cos 0 = 1$ et $\cos \frac{\pi}{2} = 0$, donc les bornes sont inversées, et on doit changer le signe.
+
+$\displaystyle\frac{dt}{dx} = - \frac{1}{\sqrt{ 1-x^{2} }}$ donc $\displaystyle dt = - \frac{dx}{\sqrt{ 1-x^{2} }}$
+