Sr Examen
Integral de x^(1/2)cosx dx
Solución
Ha introducido
[src]
1 / | | ___ | \/ x *cos(x) dx | / 0
$$\int\limits_{0}^{1} \sqrt{x} \cos{\left(x \right)}\, dx$$
Integral(sqrt(x)*cos(x), (x, 0, 1))
Respuesta (Indefinida)
[src]
_ / | 2 \
/ 3/2 |_ | 1/4, 3/4 | -x |
| / ___ ___\ x *Gamma(1/4)*Gamma(3/4)* | | | ----|
| ___ ___ ____ |\/ 2 *\/ x | 2 3 \1/2, 5/4, 7/4 | 4 /
| \/ x *cos(x) dx = C + x*\/ 2 *\/ pi *C|-----------| - ------------------------------------------------------
| | ____ | 4*Gamma(5/4)*Gamma(7/4)
/ \ \/ pi /
$$\int \sqrt{x} \cos{\left(x \right)}\, dx = C - \frac{x^{\frac{3}{2}} \Gamma\left(\frac{1}{4}\right) \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{3}\left(\begin{matrix} \frac{1}{4}, \frac{3}{4} \\ \frac{1}{2}, \frac{5}{4}, \frac{7}{4} \end{matrix}\middle| {- \frac{x^{2}}{4}} \right)}}{4 \Gamma\left(\frac{5}{4}\right) \Gamma\left(\frac{7}{4}\right)} + \sqrt{2} \sqrt{\pi} x C\left(\frac{\sqrt{2} \sqrt{x}}{\sqrt{\pi}}\right)$$
Gráfica
Respuesta
[src]
/ ___ \
___ ____ |\/ 2 |
3*\/ 2 *\/ pi *S|------|*Gamma(3/4)
| ____|
3*Gamma(3/4)*sin(1) \\/ pi /
------------------- - -----------------------------------
4*Gamma(7/4) 8*Gamma(7/4)
$$- \frac{3 \sqrt{2} \sqrt{\pi} S\left(\frac{\sqrt{2}}{\sqrt{\pi}}\right) \Gamma\left(\frac{3}{4}\right)}{8 \Gamma\left(\frac{7}{4}\right)} + \frac{3 \sin{\left(1 \right)} \Gamma\left(\frac{3}{4}\right)}{4 \Gamma\left(\frac{7}{4}\right)}$$
=
=
/ ___ \
___ ____ |\/ 2 |
3*\/ 2 *\/ pi *S|------|*Gamma(3/4)
| ____|
3*Gamma(3/4)*sin(1) \\/ pi /
------------------- - -----------------------------------
4*Gamma(7/4) 8*Gamma(7/4)
$$- \frac{3 \sqrt{2} \sqrt{\pi} S\left(\frac{\sqrt{2}}{\sqrt{\pi}}\right) \Gamma\left(\frac{3}{4}\right)}{8 \Gamma\left(\frac{7}{4}\right)} + \frac{3 \sin{\left(1 \right)} \Gamma\left(\frac{3}{4}\right)}{4 \Gamma\left(\frac{7}{4}\right)}$$
3*gamma(3/4)*sin(1)/(4*gamma(7/4)) - 3*sqrt(2)*sqrt(pi)*fresnels(sqrt(2)/sqrt(pi))*gamma(3/4)/(8*gamma(7/4))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.