Question

ayudaaaaaa \int_{3}^{5}{\frac{x}{30-x^2}}\ dx

Answer 1

Respuesta:

Explicación:

$\int\limits^5_3 {\frac{x}{30-x^{2} } } \, dx // \\cambio \ de\ variable\\\\u=30-x^{2} \ \ \frac{du}{dx} =-2x \\ \frac{du}{ -2x } =dx\\\\-\frac{1}{2} \ \int\limits^5_3 {\frac{du}{u} } \, \\\\cambiamos \ limites\ de\ integracion\\\\\\\\x=3 \ 30-x^{2} =21 \ limite\ inferior\\\\x=5 \ \ 30-x^{2} =5 \ limite \ superior\\\\\\-\frac{1}{2} \ \int\limits^5_21 {\frac{du}{u} } \, dx =ln[u] \\\\evaluamos\ de \ 21 \ a \ 5 \\\\-\frac{1}{2} (ln[5] - ln[21]) \\\\-\frac{1}{2} (ln\frac{5}{21} )=0.7175 \ u^{2}$