Calcolare l'integrale definito da -1 a 1 della funzione f(x) = x²/[1 - e^(-x)]
1/3 ma arrivo tardi.
int_(-1)^1 x^2/(1-e^(-x))dx
=int_(-1)^0 x^2(1-e^(-x))dx
+int_0^1 x^2/(1-e^(-x))dx
=int_0^1 t^2/(1-e^t)dt
+int_0^1 x^2/(1-e^(-x))dx
=int_0^1
t^2 e^(-t)/(e^(-t)-1)dt
+int_0^1 x^2/(1-e^(-x))dx
=int_0^1x^2dx
=1/3.
Applicato professionalmente
Convincente
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