Sr Examen
Integral de (1-x^4)^(1/2) dx
Solución
Ha introducido
[src]
1 / | | ________ | / 4 | \/ 1 - x dx | / 0
$$\int\limits_{0}^{1} \sqrt{1 - x^{4}}\, dx$$
Integral(sqrt(1 - x^4), (x, 0, 1))
Respuesta (Indefinida)
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/ _ | |_ /-1/2, 1/4 | 4 2*pi*I\ | ________ x*Gamma(1/4)* | | | x *e | | / 4 2 1 \ 5/4 | / | \/ 1 - x dx = C + ------------------------------------------ | 4*Gamma(5/4) /
$$\int \sqrt{1 - x^{4}}\, dx = C + \frac{x \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle| {x^{4} e^{2 i \pi}} \right)}}{4 \Gamma\left(\frac{5}{4}\right)}$$
Gráfica
Respuesta
[src]
_
|_ /-1/2, 1/4 | \
Gamma(1/4)* | | | 1|
2 1 \ 5/4 | /
-------------------------------
4*Gamma(5/4)
$$\frac{\Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle| {1} \right)}}{4 \Gamma\left(\frac{5}{4}\right)}$$
=
=
_
|_ /-1/2, 1/4 | \
Gamma(1/4)* | | | 1|
2 1 \ 5/4 | /
-------------------------------
4*Gamma(5/4)
$$\frac{\Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle| {1} \right)}}{4 \Gamma\left(\frac{5}{4}\right)}$$
gamma(1/4)*hyper((-1/2, 1/4), (5/4,), 1)/(4*gamma(5/4))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.