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