Question

Salut, am si eu nevoie de ajutor la ex. 994( explicatii pas cu pas)

Answer 1

$f(x) = e^{-x} > 0 \\ f(x) = e^{x} > 0 \\ \\\text{Nu ne intereseaza care functie e deasupra celeilalte,} \\ \text{punem modul si nu mai e nevoie.}\\ \\ \Rightarrow A = \displaystyle \left|\int_{0}^1\Big[f(x)-g(x)\Big]\, dx\right| \\ \\ \int_{0}^1\Big[f(x)-g(x)\Big]\, dx = \int_{0}^1 (e^{-x}-e^{x})\, dx = (-e^{-x}- e^{x})\Big|_{0}^1 = \\ \\ = -e^{-1}-e+1+1= -e^{-1}-e+2 \\ \\ \Rightarrow A = |-e^{-1}-e+2| = e+\dfrac{1}{e}-2$