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Resolución de integrales/ x^2/2/ cos(x^2/2)/x^2

Integral de cos(x^2/2)/x^2 dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
 1/2          
  /           
 |            
 |     / 2\   
 |     |x |   
 |  cos|--|   
 |     \2 /   
 |  ------- dx
 |      2     
 |     x      
 |            
/             
1/4
$$\int\limits_{\frac{1}{4}}^{\frac{1}{2}} \frac{\cos{\left(\frac{x^{2}}{2} \right)}}{x^{2}}\, dx$$ 
Integral(cos(x^2/2)/x^2, (x, 1/4, 1/2))
Respuesta (Indefinida) [src] 
  /                   /          
 |                   |           
 |    / 2\           |    / 2\   
 |    |x |           |    |x |   
 | cos|--|           | cos|--|   
 |    \2 /           |    \2 /   
 | ------- dx = C +  | ------- dx
 |     2             |     2     
 |    x              |    x      
 |                   |           
/                   /
$$\int \frac{\cos{\left(\frac{x^{2}}{2} \right)}}{x^{2}}\, dx = C + \int \frac{\cos{\left(\frac{x^{2}}{2} \right)}}{x^{2}}\, dx$$
Simplificar
Gráfica
Trazar el gráfico f(x)
Respuesta [src] 
                                                 ____  /   1    \                 ____  /   1    \            
                                               \/ pi *S|--------|*Gamma(-1/4)   \/ pi *S|--------|*Gamma(-1/4)
                                                       |    ____|                       |    ____|            
cos(1/8)*Gamma(-1/4)   cos(1/32)*Gamma(-1/4)           \4*\/ pi /                       \2*\/ pi /            
-------------------- - --------------------- - ------------------------------ + ------------------------------
    2*Gamma(3/4)             Gamma(3/4)                 4*Gamma(3/4)                     4*Gamma(3/4)
$$\frac{\cos{\left(\frac{1}{8} \right)} \Gamma\left(- \frac{1}{4}\right)}{2 \Gamma\left(\frac{3}{4}\right)} + \frac{\sqrt{\pi} S\left(\frac{1}{2 \sqrt{\pi}}\right) \Gamma\left(- \frac{1}{4}\right)}{4 \Gamma\left(\frac{3}{4}\right)} - \frac{\sqrt{\pi} S\left(\frac{1}{4 \sqrt{\pi}}\right) \Gamma\left(- \frac{1}{4}\right)}{4 \Gamma\left(\frac{3}{4}\right)} - \frac{\cos{\left(\frac{1}{32} \right)} \Gamma\left(- \frac{1}{4}\right)}{\Gamma\left(\frac{3}{4}\right)}$$ 
=
= 
                                                 ____  /   1    \                 ____  /   1    \            
                                               \/ pi *S|--------|*Gamma(-1/4)   \/ pi *S|--------|*Gamma(-1/4)
                                                       |    ____|                       |    ____|            
cos(1/8)*Gamma(-1/4)   cos(1/32)*Gamma(-1/4)           \4*\/ pi /                       \2*\/ pi /            
-------------------- - --------------------- - ------------------------------ + ------------------------------
    2*Gamma(3/4)             Gamma(3/4)                 4*Gamma(3/4)                     4*Gamma(3/4)
$$\frac{\cos{\left(\frac{1}{8} \right)} \Gamma\left(- \frac{1}{4}\right)}{2 \Gamma\left(\frac{3}{4}\right)} + \frac{\sqrt{\pi} S\left(\frac{1}{2 \sqrt{\pi}}\right) \Gamma\left(- \frac{1}{4}\right)}{4 \Gamma\left(\frac{3}{4}\right)} - \frac{\sqrt{\pi} S\left(\frac{1}{4 \sqrt{\pi}}\right) \Gamma\left(- \frac{1}{4}\right)}{4 \Gamma\left(\frac{3}{4}\right)} - \frac{\cos{\left(\frac{1}{32} \right)} \Gamma\left(- \frac{1}{4}\right)}{\Gamma\left(\frac{3}{4}\right)}$$ 
cos(1/8)*gamma(-1/4)/(2*gamma(3/4)) - cos(1/32)*gamma(-1/4)/gamma(3/4) - sqrt(pi)*fresnels(1/(4*sqrt(pi)))*gamma(-1/4)/(4*gamma(3/4)) + sqrt(pi)*fresnels(1/(2*sqrt(pi)))*gamma(-1/4)/(4*gamma(3/4))
Respuesta numérica [src] 
1.99544559110017
1.99544559110017

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

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