Question

Exercitiul 2 punctul b

Answer 1

f(x)=$x^{2011}(x+1)+x(x+1)=(x+1)( x^{2011} +x)$

Integrala va fi: $\int\limits^1_0 { \frac{f(x)}{x+1} } \, dx = \int\limits^1_0 ({ x^{2011}+x }) \, dx = (\frac{ x^{2012} }{2012} + \frac{ x^{2} }{2} )$  cu limitele de integrare 1 si 0 deci $\frac{1}{2012} + \frac{1}{2} = \frac{1007}{2012}$