grandes-ecoles 2015 QII.A.1

grandes-ecoles · France · centrale-maths2__mp Integration by Substitution Convergence and Evaluation of Improper Integrals
Let $x > 0$. Show that $t \mapsto t ^ { x - 1 } e ^ { - t }$ is integrable on $] 0 , + \infty [$. 
Let $x > 0$. Show that $t \mapsto t ^ { x - 1 } e ^ { - t }$ is integrable on $] 0 , + \infty [$.
Paper Questions
QI.A.1 QI.A.2 QI.B QI.C.1 QI.C.2 QI.D.1 QI.D.2 QI.D.3 QI.D.4 QI.E QI.F.1 QI.F.2 QI.F.3 QII.A.1 QII.A.2 QII.B.1 QII.B.2 QII.B.3 QII.B.4 QII.C.1 QII.C.2 QII.C.3 QII.C.4 QII.C.5 QII.C.6 QII.C.7 QII.C.8 QIII.A QIII.B.1 QIII.B.2 QIII.B.3 QIII.C.1 QIII.C.2 QIII.C.3 QIII.D.1 QIII.D.2 QIII.D.3 QIV.A QIV.B.1 QIV.B.2 QIV.B.3 QIV.B.4 QIV.C.1 QIV.C.2