[m]e^{-\frac{x}{4}}=1+(-\frac{x}{4})+\frac{(-\frac{x}{4})^2}{2!}+\frac{(-\frac{x}{4})^3}{3!}+...+\frac{(-\frac{x}{4})^n}{n!}+...[/m]
[m]\sqrt{x}\cdot e^{-\frac{x}{4}}=\sqrt{x}\cdot (1+(-\frac{x}{4})+\frac{(-\frac{x}{4})^2}{2!}+\frac{(-\frac{x}{4})^3}{3!}+...+\frac{(-\frac{x}{4})^n}{n!}+...)[/m]
[m]\sqrt{x}=x^{\frac{1}{2}}[/m]
[m]\sqrt{x}\cdot e^{-\frac{x}{4}}=x^{\frac{1}{2}}-\frac{x^{\frac{3}{2}}}{4}+\frac{x^{\frac{5}{2}}}{16}+\frac{x^{\frac{7}{2}}}{384}+...[/m]
[m] ∫^{0,4}_{0} \sqrt{x}\cdot e^{-\frac{x}{4}}dx ∫^{0,4}_{0}(x^{\frac{1}{2}}-\frac{x^{\frac{3}{2}}}{4}+\frac{x^{\frac{5}{2}}}{16}+\frac{x^{\frac{7}{2}}}{384}+...)dx=(\frac{x^{\frac{3}{2}}}{\frac{3}{2}} -\frac{x^{\frac{5}{2}}}{4\cdot \frac{5}{2}}+\frac{x^{\frac{7}{2}}}{4\cdot \frac{7}{2}}+...)|^{0,4}_{0}=\frac{2}{3}0,4^{\frac{3}{2}}-\frac{1}{10}0,4^{\frac{5}{2}}+\frac{1}{14}0,4^{\frac{7}{2}}+...[/m]