Răspuns:
Explicație pas cu pas:
[tex]a)\displaystyle\int_1^2\dfrac{f(x)}{x}dx=\int_1^2 \dfrac{x\cdot e^x}{x}dx=\int_1^2e^xdx=e^x|_1^2=e^2-e=e(e-1)\\c)\texttt{Se aplica schimbarea de variabila }f(x)=t\Rightarrow f'(x)dx=dt\\\int_0^etdt=\dfrac{t^2}{2}|_0^e=\dfrac{e^2}{2}-\dfrac{0}{2}=\dfrac{e^2}{2},\texttt{ deci }a=2[/tex]
