grandes-ecoles 2022 Q13

grandes-ecoles · France · centrale-maths2__psi Reduction Formulae Compute a Base Case or Specific Value of a Parametric Integral

Show that, for all $k \in \mathbb { N } , \int _ { 0 } ^ { + \infty } t ^ { k } \mathrm { e } ^ { - t } \mathrm {~d} t = k !$.

Show that, for all $k \in \mathbb { N } , \int _ { 0 } ^ { + \infty } t ^ { k } \mathrm { e } ^ { - t } \mathrm {~d} t = k !$.