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Resolución de integrales/ (x)^1/2/ sinx/(x*(x)^1/2)

Integral de sinx/(x*(x)^1/2) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

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)                                         
 |                                                                             
/
$$\int \frac{\sin{\left(x \right)}}{\sqrt{x} x}\, dx = C + \frac{\sqrt{2} \sqrt{\pi} C\left(\frac{\sqrt{2} \sqrt{x}}{\sqrt{\pi}}\right) \Gamma\left(\frac{1}{4}\right)}{2 \Gamma\left(\frac{5}{4}\right)} - \frac{\sin{\left(x \right)} \Gamma\left(\frac{1}{4}\right)}{2 \sqrt{x} \Gamma\left(\frac{5}{4}\right)}$$
Simplificar
Gráfica
Trazar el gráfico f(x)
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))
Respuesta numérica [src] 
1.73662738956295
1.73662738956295

    Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.

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