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Resolución de integrales/ x^2+4/ cos(3x^2+4)

Integral de cos(3x^2+4) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                 
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 |  cos\3*x  + 4/ dx
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0
∫01cos⁡(3x2+4) dx\int\limits_{0}^{1} \cos{\left(3 x^{2} + 4 \right)}\, dx 
Integral(cos(3*x^2 + 4), (x, 0, 1))
Solución detallada

    FresnelCRule(a=3, b=0, c=4, context=cos(3*x**2 + 4), symbol=x)

  1. Añadimos la constante de integración:

    6π(cos⁡(4)C(6xπ)−sin⁡(4)S(6xπ))6+constant\frac{\sqrt{6} \sqrt{\pi} \left(\cos{\left(4 \right)} C\left(\frac{\sqrt{6} x}{\sqrt{\pi}}\right) - \sin{\left(4 \right)} S\left(\frac{\sqrt{6} x}{\sqrt{\pi}}\right)\right)}{6}+ \mathrm{constant}

Respuesta:

6π(cos⁡(4)C(6xπ)−sin⁡(4)S(6xπ))6+constant\frac{\sqrt{6} \sqrt{\pi} \left(\cos{\left(4 \right)} C\left(\frac{\sqrt{6} x}{\sqrt{\pi}}\right) - \sin{\left(4 \right)} S\left(\frac{\sqrt{6} x}{\sqrt{\pi}}\right)\right)}{6}+ \mathrm{constant}

Respuesta (Indefinida) [src] 
                                       /        /    ___\    /    ___\       \
                            ___   ____ |        |x*\/ 6 |    |x*\/ 6 |       |
  /                       \/ 6 *\/ pi *|cos(4)*C|-------| - S|-------|*sin(4)|
 |                                     |        |   ____|    |   ____|       |
 |    /   2    \                       \        \ \/ pi /    \ \/ pi /       /
 | cos\3*x  + 4/ dx = C + ----------------------------------------------------
 |                                                 6                          
/
∫cos⁡(3x2+4) dx=C+6π(cos⁡(4)C(6xπ)−sin⁡(4)S(6xπ))6\int \cos{\left(3 x^{2} + 4 \right)}\, dx = C + \frac{\sqrt{6} \sqrt{\pi} \left(\cos{\left(4 \right)} C\left(\frac{\sqrt{6} x}{\sqrt{\pi}}\right) - \sin{\left(4 \right)} S\left(\frac{\sqrt{6} x}{\sqrt{\pi}}\right)\right)}{6}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.902-2
Trazar el gráfico f(x)
Respuesta [src] 
             /        /  ___ \    /  ___ \       \
  ___   ____ |        |\/ 6  |    |\/ 6  |       |
\/ 6 *\/ pi *|cos(4)*C|------| - S|------|*sin(4)|
             |        |  ____|    |  ____|       |
             \        \\/ pi /    \\/ pi /       /
--------------------------------------------------
                        6
6π(cos⁡(4)C(6π)−sin⁡(4)S(6π))6\frac{\sqrt{6} \sqrt{\pi} \left(\cos{\left(4 \right)} C\left(\frac{\sqrt{6}}{\sqrt{\pi}}\right) - \sin{\left(4 \right)} S\left(\frac{\sqrt{6}}{\sqrt{\pi}}\right)\right)}{6} 
=
= 
             /        /  ___ \    /  ___ \       \
  ___   ____ |        |\/ 6  |    |\/ 6  |       |
\/ 6 *\/ pi *|cos(4)*C|------| - S|------|*sin(4)|
             |        |  ____|    |  ____|       |
             \        \\/ pi /    \\/ pi /       /
--------------------------------------------------
                        6
6π(cos⁡(4)C(6π)−sin⁡(4)S(6π))6\frac{\sqrt{6} \sqrt{\pi} \left(\cos{\left(4 \right)} C\left(\frac{\sqrt{6}}{\sqrt{\pi}}\right) - \sin{\left(4 \right)} S\left(\frac{\sqrt{6}}{\sqrt{\pi}}\right)\right)}{6} 
sqrt(6)*sqrt(pi)*(cos(4)*fresnelc(sqrt(6)/sqrt(pi)) - fresnels(sqrt(6)/sqrt(pi))*sin(4))/6
Respuesta numérica [src] 
0.124385348693692
0.124385348693692

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

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