Sr Examen
Integral de |sinx|/x^p dx
Solución
Ha introducido
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1 / | | |sin(x)| | -------- dx | p | x | / 0
$$\int\limits_{0}^{1} \frac{\left|{\sin{\left(x \right)}}\right|}{x^{p}}\, dx$$
Integral(Abs(sin(x))/x^p, (x, 0, 1))
Respuesta (Indefinida)
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/ / | | | |sin(x)| | -p | -------- dx = C + | x *|sin(x)| dx | p | | x / | /
$$\int \frac{\left|{\sin{\left(x \right)}}\right|}{x^{p}}\, dx = C + \int x^{- p} \left|{\sin{\left(x \right)}}\right|\, dx$$
Respuesta
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/ p | \
_ | 1 - - | |
/ p\ |_ | 2 | |
Gamma|1 - -|* | | | -1/4|
\ 2/ 1 2 | p | |
|3/2, 2 - - | |
\ 2 | /
-------------------------------------
/ p\
2*Gamma|2 - -|
\ 2/
$$\frac{\Gamma\left(1 - \frac{p}{2}\right) {{}_{1}F_{2}\left(\begin{matrix} 1 - \frac{p}{2} \\ \frac{3}{2}, 2 - \frac{p}{2} \end{matrix}\middle| {- \frac{1}{4}} \right)}}{2 \Gamma\left(2 - \frac{p}{2}\right)}$$
=
=
/ p | \
_ | 1 - - | |
/ p\ |_ | 2 | |
Gamma|1 - -|* | | | -1/4|
\ 2/ 1 2 | p | |
|3/2, 2 - - | |
\ 2 | /
-------------------------------------
/ p\
2*Gamma|2 - -|
\ 2/
$$\frac{\Gamma\left(1 - \frac{p}{2}\right) {{}_{1}F_{2}\left(\begin{matrix} 1 - \frac{p}{2} \\ \frac{3}{2}, 2 - \frac{p}{2} \end{matrix}\middle| {- \frac{1}{4}} \right)}}{2 \Gamma\left(2 - \frac{p}{2}\right)}$$
gamma(1 - p/2)*hyper((1 - p/2,), (3/2, 2 - p/2), -1/4)/(2*gamma(2 - p/2))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.