Question

Integrala de la 0 la 1 din x inmultit cu e la puterea minus x patrat. Va rog

Answer 1

[tex] \int\limits^1_0 {x* e^{-x^2} } \, dx= \\ \\ ux=-x^2 \\ \\ u'x=-2x \\ \\ - \frac{1}{2} \int\limits^1_0 {u'x* e^{ux} } \, dx =- \frac{1}{2} e^{-x^2} |^1_0= -\frac{1}{2} ( e^{-1} -1)= -\frac{1}{2} ( \frac{1}{e} -1) [/tex]