1 year ago

(07.08 LC)

Mathematics

1 answer:

Brut [27]1 year ago

3 0

Answer:

Step-by-step explanation:

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Step-by-step explanation:

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Haya la integral de xarcsenx/((1-x^2)^1/2). Utiliza la sustitución de t= arcsenx

ikadub [295]

Answer:

<em>Explicación más abajo</em>

Step-by-step explanation:

Integración Indefinida

La integral

$I=\int \dfrac{x .arcsen\left(x\right)}{\sqrt{1-x^2}}$

Se resuelve con el cambio de variables:

t=arcsen(x)

Una vez hechos los cambios, la integral se resuelve en función de t:

$I=sen(t)-t.cos(t)+C$

Hay que devolver los cambios para mostrarla en función de x.

El cambio de variables también se puede escribir:

x=sen(t)

Recordando que

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Entonces:

$cos(t)=\sqrt{1-x^2}$

Devolviendo los cambios:

$I=sen(t)-t.cos(t)+C=x-arcsen(x)\sqrt{1-x^2}+C$

Es la respuesta correcta

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2 years ago

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Step-by-step explanation:

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