grandes-ecoles 2016 QII.E

grandes-ecoles · France · centrale-maths2__psi First order differential equations (integrating factor)

Prove that $\forall x \in \mathbb{R}, \quad \int_{-\infty}^{+\infty} \frac{e^{2\pi\mathrm{i} x\xi}}{1+(2\pi\xi)^{2}} \mathrm{d}\xi = \frac{1}{2} e^{-|x|}$.

Prove that $\forall x \in \mathbb{R}, \quad \int_{-\infty}^{+\infty} \frac{e^{2\pi\mathrm{i} x\xi}}{1+(2\pi\xi)^{2}} \mathrm{d}\xi = \frac{1}{2} e^{-|x|}$.

Paper Questions

QI.A QI.B QI.C QI.D QI.E QII.A QII.B QII.C QII.D QII.E QIII.A QIII.B QIII.C QIV.A QIV.B QIV.C QIV.D QIV.E QIV.F QIV.G QV.A QV.B QV.C QV.D QV.E QVI.A QVI.B QVI.C