Question

Se considera functia f:R=>R , f(x)=$e^{x} -x$
a) Sa se verifice ca $\int\limits^1_0 {f(x)} \, dx = e- \frac{3}{2}$
Multumesc mult! 

Answer 1

[tex] \int\limits^1_0 {f(x)} \, dx = \int\limits^1_0 {(e^x-x)} \, dx = \int\limits^1_0 {e^x} \, dx - \int\limits^1_0 {x} \, dx =\\ =e^x|_0^1- \frac{x^2}{2}|_0^1 =\\ =(e^1-e^0)-( \frac{1^2}{2} - \frac{0^2}{2})=\\ =(e-1)- \frac{1}{2} =\\ =e- \frac{3}{2} [/tex]