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# System prepended metadata

title: Exo maths zeta de 2

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Exo maths zeta de 2
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$u(x) = \dfrac{-cos(nt)}{n^2}$

$v(x) = \dfrac{sin(nt)}{n}$

$cos(nt)$

$$\int_0^{\pi}(a x^2+bx+c)cos(nx)dx$$


$$\int_0^{\pi}x^2cos(nt)+\int_0^{\pi}xcos(nt)$$


$\int u'v=[uv]-\int uv'$


$\displaystyle - \dfrac{2}{n}\int_0^{\pi}xsin(nt)$     $\displaystyle - \int_0^{\pi}\sin(nt)$\\

$\displaystyle [\dfrac{cos(nt)}{n}]_0^{\pi}=\dfrac{1}{n}+\dfrac{-1^n}{n}$

$\int_0^{\pi}x^2cos(nt)dt = \dfrac{2}{n^2} + \dfrac{2\cdot (-1)^n}{n^2}$

$\int_0^{\pi}xcos(nt)dt = \dfrac{(-1)^n}{n^2} + \dfrac{2\cdot (-1)^n}{n^2}$

