☛ Utiliser la linéarité

Énoncé
Calculer  \(\displaystyle I=\int_1^2 \left(\dfrac 2 x+\text e^{-x}\right) \text d x\) .

Solution

\(\begin{array}{rcl}I &= & \displaystyle \int_1^2 \left(\dfrac 2 x+\text e^{-x}\right) \text d x \\I &= & \displaystyle 2\int_1^2 \dfrac 1 x\text d x + \int_1^2\text e^{-x}\text d x \\\displaystyle I &= & 2 \times \Big[\ln(x)\Big]_1^2+\Big[-\text e^{-x}\Big]_1^2\\\displaystyle I &= &2\ln(2)+\text e^{-1}-\text e^{-2}\\\end{array}\)