Răspuns:
Explicație pas cu pas:
Se face schimbarea nx²=t.
[tex]nx^2=t\\2ndx=dt\\dx=\frac{dt}{2n}[/tex]
Mai departe e simplu.
[tex]\displaystyle I_n=\frac{1}{2n}\int_0^ne^{-t}dt=-\frac{e^{-t}}{2n}|_0^n=-\dfrac{e^{-n}}{2n}+\dfrac{e^{-0}}{2n}=\dfrac{1}{2n}(1-\dfrac{1}{e^n})[/tex]
