Определени интеграли

[dilyan_nikoloff]

[tex]\int_{0}^{2} \frac{3}{x-3 }[/tex]

[tex]\int_{2}^{ 3} 2x^{2}-3x+1[/tex]

Ако може някой да помогне

[martin123456]

1
[tex]\int_{0}^{2}\frac{3}{x-3}dx=3\int_{0}^{2}\frac{1}{x-3}dx=3\int_{0}^{2}\frac{1}{x-3}d(x-3)=3\ln{|x-3|}|_{0}^{2}=3(\ln1-\ln3)=3\ln3[/tex]
2
[tex]\int_{2}^{3}(2x^2-3x+1)dx=2\int_{2}^{3}x^2dx-3\int_{2}^{3}x+\int_{2}^{3}dx=2\frac{x^3}{3}|_{2}^{3}-3\frac{x^2}{2}|_{2}^{3}+x|_{2}^{3}=..[/tex]