Sr Examen
Integral de sin(t^4) dx
Solución
Ha introducido
[src]
1 / | | / 4\ | sin\t / dt | / 0
$$\int\limits_{0}^{1} \sin{\left(t^{4} \right)}\, dt$$
Integral(sin(t^4), (t, 0, 1))
Respuesta (Indefinida)
[src]
_ / | 8 \
/ 5 |_ | 5/8 | -t |
| t *Gamma(5/8)* | | | ----|
| / 4\ 1 2 \3/2, 13/8 | 4 /
| sin\t / dt = C + -------------------------------------
| 8*Gamma(13/8)
/
$$\int \sin{\left(t^{4} \right)}\, dt = C + \frac{t^{5} \Gamma\left(\frac{5}{8}\right) {{}_{1}F_{2}\left(\begin{matrix} \frac{5}{8} \\ \frac{3}{2}, \frac{13}{8} \end{matrix}\middle| {- \frac{t^{8}}{4}} \right)}}{8 \Gamma\left(\frac{13}{8}\right)}$$
Gráfica
Respuesta
[src]
_
|_ / 5/8 | \
Gamma(5/8)* | | | -1/4|
1 2 \3/2, 13/8 | /
----------------------------------
8*Gamma(13/8)
$$\frac{\Gamma\left(\frac{5}{8}\right) {{}_{1}F_{2}\left(\begin{matrix} \frac{5}{8} \\ \frac{3}{2}, \frac{13}{8} \end{matrix}\middle| {- \frac{1}{4}} \right)}}{8 \Gamma\left(\frac{13}{8}\right)}$$
=
=
_
|_ / 5/8 | \
Gamma(5/8)* | | | -1/4|
1 2 \3/2, 13/8 | /
----------------------------------
8*Gamma(13/8)
$$\frac{\Gamma\left(\frac{5}{8}\right) {{}_{1}F_{2}\left(\begin{matrix} \frac{5}{8} \\ \frac{3}{2}, \frac{13}{8} \end{matrix}\middle| {- \frac{1}{4}} \right)}}{8 \Gamma\left(\frac{13}{8}\right)}$$
gamma(5/8)*hyper((5/8,), (3/2, 13/8), -1/4)/(8*gamma(13/8))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.