Question

Resulve la integral indefinida :


$\displaystyle\int\dfrac{x^{2}}{2}~~dx$

Answer 1

¡Hola!

Resulve la integral indefinida :

$\displaystyle\int\dfrac{x^{2}}{2}\:dx$

solución:

*  vamos a resolver $\displaystyle\int \dfrac{x^2}{2}\:dx$

$\dfrac{1}{2}*\displaystyle\int x^2}\:dx$

Por la regla de potencia

$\displaystyle\int x^a\:dx=\dfrac{x^{a+1}}{a+1}$ , si: a≠-1

$\displaystyle\int\dfrac{x^{2}}{2}\:dx =\dfrac{1}{2}*\int x^2}dx$

$\displaystyle\int\dfrac{x^{2}}{2}\:dx =\dfrac{1}{2}*\dfrac{x^{2+1}}{2+1}$

$\displaystyle\int\dfrac{x^{2}}{2}\:dx =\dfrac{1}{2}*\dfrac{x^3}{3}$

$\displaystyle\int\dfrac{x^{2}}{2}\:dx = \dfrac{1*x^{3}}{2*3}$

$\displaystyle\int\dfrac{x^{2}}{2}\:dx = \dfrac{x^3}{6}$

En integrales indefinidas, añadimos una constante (C), veamos:

$\displaystyle\int\dfrac{x^{2}}{2}\:dx=\boxed{\boxed{\dfrac{x^3}{6}+C}}\:\:\:\:\:\:\bf\green{\checkmark}$

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