Sr Examen

Otras calculadoras

Resolución de integrales/ ((b^2-a^2)*cos(x)*sin(x)+(a^3*b+b^3*a)*(cos(x)*sin(x))^2+a*b*(b^2*sin(x)^4+a^2*cos(x)^4))/(a^2*cos(x)^2+b^2*sin(x)^2)

Integral de ((b^2-a^2)*cos(x)*sin(x)+(a^3*b+b^3*a)*(cos(x)*sin(x))^2+a*b*(b^2*sin(x)^4+a^2*cos(x)^4))/(a^2*cos(x)^2+b^2*sin(x)^2) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                                                                                            
  /                                                                                            
 |                                                                                             
 |  / 2    2\                 / 3      3  \                2       / 2    4       2    4   \   
 |  \b  - a /*cos(x)*sin(x) + \a *b + b *a/*(cos(x)*sin(x))  + a*b*\b *sin (x) + a *cos (x)/   
 |  ---------------------------------------------------------------------------------------- dx
 |                                   2    2       2    2                                       
 |                                  a *cos (x) + b *sin (x)                                    
 |                                                                                             
/                                                                                              
0
$$\int\limits_{0}^{1} \frac{a b \left(a^{2} \cos^{4}{\left(x \right)} + b^{2} \sin^{4}{\left(x \right)}\right) + \left(\left(- a^{2} + b^{2}\right) \cos{\left(x \right)} \sin{\left(x \right)} + \left(\sin{\left(x \right)} \cos{\left(x \right)}\right)^{2} \left(a^{3} b + a b^{3}\right)\right)}{a^{2} \cos^{2}{\left(x \right)} + b^{2} \sin^{2}{\left(x \right)}}\, dx$$ 
Integral((((b^2 - a^2)*cos(x))*sin(x) + (a^3*b + b^3*a)*(cos(x)*sin(x))^2 + (a*b)*(b^2*sin(x)^4 + a^2*cos(x)^4))/(a^2*cos(x)^2 + b^2*sin(x)^2), (x, 0, 1))
Respuesta [src] 
/   /           2    2   \                                                              
|   |   2      b *sin (1)|                                                              
|log|cos (1) + ----------|                                                              
|   |               2    |                                                              
<   \              a     /          2             2                                     
|------------------------- + a*b*cos (1) + a*b*sin (1)  for And(a > -oo, a < oo, a != 0)
|            2                                                                          
|                                                                                       
\                         oo                                       otherwise
$$\begin{cases} a b \cos^{2}{\left(1 \right)} + a b \sin^{2}{\left(1 \right)} + \frac{\log{\left(\cos^{2}{\left(1 \right)} + \frac{b^{2} \sin^{2}{\left(1 \right)}}{a^{2}} \right)}}{2} & \text{for}\: a > -\infty \wedge a < \infty \wedge a \neq 0 \\\infty & \text{otherwise} \end{cases}$$ 
=
= 
/   /           2    2   \                                                              
|   |   2      b *sin (1)|                                                              
|log|cos (1) + ----------|                                                              
|   |               2    |                                                              
<   \              a     /          2             2                                     
|------------------------- + a*b*cos (1) + a*b*sin (1)  for And(a > -oo, a < oo, a != 0)
|            2                                                                          
|                                                                                       
\                         oo                                       otherwise
$$\begin{cases} a b \cos^{2}{\left(1 \right)} + a b \sin^{2}{\left(1 \right)} + \frac{\log{\left(\cos^{2}{\left(1 \right)} + \frac{b^{2} \sin^{2}{\left(1 \right)}}{a^{2}} \right)}}{2} & \text{for}\: a > -\infty \wedge a < \infty \wedge a \neq 0 \\\infty & \text{otherwise} \end{cases}$$ 
Piecewise((log(cos(1)^2 + b^2*sin(1)^2/a^2)/2 + a*b*cos(1)^2 + a*b*sin(1)^2, (a > -oo)∧(a < oo)∧(Ne(a, 0))), (oo, True))

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

    © Sr Examen