Question

Punctul c)
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Answer 1

Răspuns:

Explicație pas cu pas:

Se face schimbarea nx²=t.

$nx^2=t\\2ndx=dt\\dx=\frac{dt}{2n}$

Mai departe e simplu.

$\displaystyle I_n=\frac{1}{2n}\int_0^ne^{-t}dt=-\frac{e^{-t}}{2n}|_0^n=-\dfrac{e^{-n}}{2n}+\dfrac{e^{-0}}{2n}=\dfrac{1}{2n}(1-\dfrac{1}{e^n})$