Răspuns:
a) 1/2
Explicație pas cu pas:
[tex]$\int_{0}^{1}{(x+1)\frac{x}{x+1}dx=\int_{0}^{1}{xdx}=\left[\frac{x^2}{2}\right]_0^1=\frac{1^2}{2}-\frac{0^2}{2}=\frac{1}{2}.$[/tex]
[tex]$\int_{0}^{1}{x^2f(x)dx}+\int_{0}^{1}{x^3f(x)dx}=\int_{0}^{1}{(x^2+x^3)f(x)dx}=\int_{0}^{1}{x^2(1+x)\frac{x}{x+1}dx}=\int_{0}^{1}{x^3dx}=\frac{1}{4}$[/tex]
