Integrali definiti immediati

Testo

Calcola i seguenti integrali definiti:

• (a) $\displaystyle\int_0^1 3e^{2x}\,dx$
• (b) $\displaystyle\int_1^{e}\frac{2}{x}\,dx$
• (c) $\displaystyle\int_1^2\Big(x+\frac{1}{x^2}\Big)\,dx$

Soluzione

(a) $\Big[\tfrac32 e^{2x}\Big]_0^1=\tfrac32(e^2-1)\approx 1{,}5\cdot 6{,}389\approx 9{,}584$.

(b) $\big[2\ln x\big]_1^{e}=2(1-0)=2$.

(c) $\Big[\tfrac{x^2}{2}-\tfrac1x\Big]_1^2=\Big(2-\tfrac12\Big)-\Big(\tfrac12-1\Big)=\tfrac32+\tfrac12=2$.

$\boxed{a=\tfrac32(e^2-1)\approx 9{,}584;\ b=2;\ c=2}$

Collegamenti

Argomenti: Integrale
Concetti: Integrale definito · Primitiva
Competenze: Integrare
Tipo di esercizio: Calcolo integrale