Question

Integrala de la 0 la 1 din g(x)/f(x)dx=integrala de la 0 la 1 din x/x^2+9 dx...mai departe cum rezolv? Calculez derivatele din amandoua?

Answer 1

[tex]\it \int^1_0 \dfrac{x}{x^2+9} dx = \dfrac{1}{2} \int^1_0 \dfrac{2x}{x^2+9} dx = \dfrac{1}{2} \int^1_0 \dfrac{(x^2 +9)'}{x^2+9} dx = \dfrac{1}{2} ln(x^2+9)\Big{|} ^1_0 \\ \\ \\ = \dfrac{1}{2}( ln 10 -ln9)= \dfrac{1}{2}ln\dfrac{10}{9} [/tex]