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Resolución de integrales/ cos(x²)/ y=cos(x²)

Integral de y=cos(x²) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  9           
  /           
 |            
 |     / 2\   
 |  cos\x / dx
 |            
/             
6
∫69cos⁡(x2) dx\int\limits_{6}^{9} \cos{\left(x^{2} \right)}\, dx 
Integral(cos(x^2), (x, 6, 9))
Solución detallada

    FresnelCRule(a=1, b=0, c=0, context=cos(x**2), symbol=x)

  1. Añadimos la constante de integración:

    2πC(2xπ)2+constant\frac{\sqrt{2} \sqrt{\pi} C\left(\frac{\sqrt{2} x}{\sqrt{\pi}}\right)}{2}+ \mathrm{constant}

Respuesta:

2πC(2xπ)2+constant\frac{\sqrt{2} \sqrt{\pi} C\left(\frac{\sqrt{2} x}{\sqrt{\pi}}\right)}{2}+ \mathrm{constant}

Respuesta (Indefinida) [src] 
                                  /    ___\
                      ___   ____  |x*\/ 2 |
  /                 \/ 2 *\/ pi *C|-------|
 |                                |   ____|
 |    / 2\                        \ \/ pi /
 | cos\x / dx = C + -----------------------
 |                             2           
/
∫cos⁡(x2) dx=C+2πC(2xπ)2\int \cos{\left(x^{2} \right)}\, dx = C + \frac{\sqrt{2} \sqrt{\pi} C\left(\frac{\sqrt{2} x}{\sqrt{\pi}}\right)}{2}
Simplificar
Gráfica
6.009.006.256.506.757.007.257.507.758.008.258.508.752-2
Trazar el gráfico f(x)
Respuesta [src] 
                /    ___\                            /    ___\           
    ___   ____  |6*\/ 2 |                ___   ____  |9*\/ 2 |           
  \/ 2 *\/ pi *C|-------|*Gamma(1/4)   \/ 2 *\/ pi *C|-------|*Gamma(1/4)
                |   ____|                            |   ____|           
                \ \/ pi /                            \ \/ pi /           
- ---------------------------------- + ----------------------------------
             8*Gamma(5/4)                         8*Gamma(5/4)
−2πC(62π)Γ(14)8Γ(54)+2πC(92π)Γ(14)8Γ(54)- \frac{\sqrt{2} \sqrt{\pi} C\left(\frac{6 \sqrt{2}}{\sqrt{\pi}}\right) \Gamma\left(\frac{1}{4}\right)}{8 \Gamma\left(\frac{5}{4}\right)} + \frac{\sqrt{2} \sqrt{\pi} C\left(\frac{9 \sqrt{2}}{\sqrt{\pi}}\right) \Gamma\left(\frac{1}{4}\right)}{8 \Gamma\left(\frac{5}{4}\right)} 
=
= 
                /    ___\                            /    ___\           
    ___   ____  |6*\/ 2 |                ___   ____  |9*\/ 2 |           
  \/ 2 *\/ pi *C|-------|*Gamma(1/4)   \/ 2 *\/ pi *C|-------|*Gamma(1/4)
                |   ____|                            |   ____|           
                \ \/ pi /                            \ \/ pi /           
- ---------------------------------- + ----------------------------------
             8*Gamma(5/4)                         8*Gamma(5/4)
−2πC(62π)Γ(14)8Γ(54)+2πC(92π)Γ(14)8Γ(54)- \frac{\sqrt{2} \sqrt{\pi} C\left(\frac{6 \sqrt{2}}{\sqrt{\pi}}\right) \Gamma\left(\frac{1}{4}\right)}{8 \Gamma\left(\frac{5}{4}\right)} + \frac{\sqrt{2} \sqrt{\pi} C\left(\frac{9 \sqrt{2}}{\sqrt{\pi}}\right) \Gamma\left(\frac{1}{4}\right)}{8 \Gamma\left(\frac{5}{4}\right)} 
-sqrt(2)*sqrt(pi)*fresnelc(6*sqrt(2)/sqrt(pi))*gamma(1/4)/(8*gamma(5/4)) + sqrt(2)*sqrt(pi)*fresnelc(9*sqrt(2)/sqrt(pi))*gamma(1/4)/(8*gamma(5/4))
Respuesta numérica [src] 
0.0471970593549392
0.0471970593549392

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

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