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

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

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

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

    FresnelSRule(a=4, b=3, c=2, context=sin(4*x**2 + 3*x + 2), symbol=x)

  1. Ahora simplificar:

  2. Añadimos la constante de integración:

Respuesta:

Respuesta (Indefinida) [src] 
                                             /         /  ___          \    /  ___          \        \
                                  ___   ____ |   /23\  |\/ 2 *(3 + 8*x)|    |\/ 2 *(3 + 8*x)|    /23\|
  /                             \/ 2 *\/ pi *|cos|--|*S|---------------| + C|---------------|*sin|--||
 |                                           |   \16/  |        ____   |    |        ____   |    \16/|
 |    /   2          \                       \         \    4*\/ pi    /    \    4*\/ pi    /        /
 | sin\4*x  + 3*x + 2/ dx = C + ----------------------------------------------------------------------
 |                                                                4                                   
/
$$\int \sin{\left(\left(4 x^{2} + 3 x\right) + 2 \right)}\, dx = C + \frac{\sqrt{2} \sqrt{\pi} \left(\sin{\left(\frac{23}{16} \right)} C\left(\frac{\sqrt{2} \left(8 x + 3\right)}{4 \sqrt{\pi}}\right) + \cos{\left(\frac{23}{16} \right)} S\left(\frac{\sqrt{2} \left(8 x + 3\right)}{4 \sqrt{\pi}}\right)\right)}{4}$$
Simplificar
Gráfica
Trazar el gráfico f(x)
Respuesta [src] 
               /         /    ___ \    /    ___ \        \                /         /     ___\    /     ___\        \
    ___   ____ |   /23\  |3*\/ 2  |    |3*\/ 2  |    /23\|     ___   ____ |   /23\  |11*\/ 2 |    |11*\/ 2 |    /23\|
  \/ 2 *\/ pi *|cos|--|*S|--------| + C|--------|*sin|--||   \/ 2 *\/ pi *|cos|--|*S|--------| + C|--------|*sin|--||
               |   \16/  |    ____|    |    ____|    \16/|                |   \16/  |    ____|    |    ____|    \16/|
               \         \4*\/ pi /    \4*\/ pi /        /                \         \4*\/ pi /    \4*\/ pi /        /
- -------------------------------------------------------- + --------------------------------------------------------
                             4                                                          4
$$- \frac{\sqrt{2} \sqrt{\pi} \left(\cos{\left(\frac{23}{16} \right)} S\left(\frac{3 \sqrt{2}}{4 \sqrt{\pi}}\right) + \sin{\left(\frac{23}{16} \right)} C\left(\frac{3 \sqrt{2}}{4 \sqrt{\pi}}\right)\right)}{4} + \frac{\sqrt{2} \sqrt{\pi} \left(\cos{\left(\frac{23}{16} \right)} S\left(\frac{11 \sqrt{2}}{4 \sqrt{\pi}}\right) + \sin{\left(\frac{23}{16} \right)} C\left(\frac{11 \sqrt{2}}{4 \sqrt{\pi}}\right)\right)}{4}$$ 
=
= 
               /         /    ___ \    /    ___ \        \                /         /     ___\    /     ___\        \
    ___   ____ |   /23\  |3*\/ 2  |    |3*\/ 2  |    /23\|     ___   ____ |   /23\  |11*\/ 2 |    |11*\/ 2 |    /23\|
  \/ 2 *\/ pi *|cos|--|*S|--------| + C|--------|*sin|--||   \/ 2 *\/ pi *|cos|--|*S|--------| + C|--------|*sin|--||
               |   \16/  |    ____|    |    ____|    \16/|                |   \16/  |    ____|    |    ____|    \16/|
               \         \4*\/ pi /    \4*\/ pi /        /                \         \4*\/ pi /    \4*\/ pi /        /
- -------------------------------------------------------- + --------------------------------------------------------
                             4                                                          4
$$- \frac{\sqrt{2} \sqrt{\pi} \left(\cos{\left(\frac{23}{16} \right)} S\left(\frac{3 \sqrt{2}}{4 \sqrt{\pi}}\right) + \sin{\left(\frac{23}{16} \right)} C\left(\frac{3 \sqrt{2}}{4 \sqrt{\pi}}\right)\right)}{4} + \frac{\sqrt{2} \sqrt{\pi} \left(\cos{\left(\frac{23}{16} \right)} S\left(\frac{11 \sqrt{2}}{4 \sqrt{\pi}}\right) + \sin{\left(\frac{23}{16} \right)} C\left(\frac{11 \sqrt{2}}{4 \sqrt{\pi}}\right)\right)}{4}$$ 
-sqrt(2)*sqrt(pi)*(cos(23/16)*fresnels(3*sqrt(2)/(4*sqrt(pi))) + fresnelc(3*sqrt(2)/(4*sqrt(pi)))*sin(23/16))/4 + sqrt(2)*sqrt(pi)*(cos(23/16)*fresnels(11*sqrt(2)/(4*sqrt(pi))) + fresnelc(11*sqrt(2)/(4*sqrt(pi)))*sin(23/16))/4
Respuesta numérica [src] 
0.0624935244969771
0.0624935244969771

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

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