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Resolución de integrales/ sqrt(exp(x)^2+(-2*exp(x)*sin(x)+2*cos(x)*exp(x))^2+(-2*cos(x)*exp(x)-2*exp(x)*sin(x))^2)

Integral de sqrt(exp(x)^2+(-2*exp(x)*sin(x)+2*cos(x)*exp(x))^2+(-2*cos(x)*exp(x)-2*exp(x)*sin(x))^2) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  2                                                                               
  /                                                                               
 |                                                                                
 |      _______________________________________________________________________   
 |     /     2                               2                               2    
 |    /  / x\    /    x                    x\    /           x      x       \     
 |  \/   \e /  + \-2*e *sin(x) + 2*cos(x)*e /  + \-2*cos(x)*e  - 2*e *sin(x)/   dx
 |                                                                                
/                                                                                 
0
$$\int\limits_{0}^{2} \sqrt{\left(e^{x} \left(- 2 \cos{\left(x \right)}\right) - 2 e^{x} \sin{\left(x \right)}\right)^{2} + \left(\left(- 2 e^{x} \sin{\left(x \right)} + e^{x} 2 \cos{\left(x \right)}\right)^{2} + \left(e^{x}\right)^{2}\right)}\, dx$$ 
Integral(sqrt(exp(x)^2 + ((-2*exp(x))*sin(x) + (2*cos(x))*exp(x))^2 + ((-2*cos(x))*exp(x) - 2*exp(x)*sin(x))^2), (x, 0, 2))
Respuesta (Indefinida) [src] 
  /                                                                                                                                
 |                                                                                                                                 
 |     _______________________________________________________________________                                                     
 |    /     2                               2                               2              ________________________________________
 |   /  / x\    /    x                    x\    /           x      x       \              /      2     2*x        2     2*x    2*x 
 | \/   \e /  + \-2*e *sin(x) + 2*cos(x)*e /  + \-2*cos(x)*e  - 2*e *sin(x)/   dx = C + \/  8*cos (x)*e    + 8*sin (x)*e    + e    
 |                                                                                                                                 
/
$$\int \sqrt{\left(e^{x} \left(- 2 \cos{\left(x \right)}\right) - 2 e^{x} \sin{\left(x \right)}\right)^{2} + \left(\left(- 2 e^{x} \sin{\left(x \right)} + e^{x} 2 \cos{\left(x \right)}\right)^{2} + \left(e^{x}\right)^{2}\right)}\, dx = C + \sqrt{8 e^{2 x} \sin^{2}{\left(x \right)} + 8 e^{2 x} \cos^{2}{\left(x \right)} + e^{2 x}}$$
Simplificar
Gráfica
Trazar el gráfico f(x)
Respuesta [src] 
  2                                     
  /                                     
 |                                      
 |     ___________________________      
 |    /          2           2      x   
 |  \/  1 + 8*cos (x) + 8*sin (x) *e  dx
 |                                      
/                                       
0
$$\int\limits_{0}^{2} \sqrt{8 \sin^{2}{\left(x \right)} + 8 \cos^{2}{\left(x \right)} + 1} e^{x}\, dx$$ 
=
= 
  2                                     
  /                                     
 |                                      
 |     ___________________________      
 |    /          2           2      x   
 |  \/  1 + 8*cos (x) + 8*sin (x) *e  dx
 |                                      
/                                       
0
$$\int\limits_{0}^{2} \sqrt{8 \sin^{2}{\left(x \right)} + 8 \cos^{2}{\left(x \right)} + 1} e^{x}\, dx$$ 
Integral(sqrt(1 + 8*cos(x)^2 + 8*sin(x)^2)*exp(x), (x, 0, 2))
Respuesta numérica [src] 
19.1671682967919
19.1671682967919

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

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