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Resolución de integrales/ abs((4+2*sin(0,1x)+3*x^2*sin(1,2*x)))

Integral de abs((4+2*sin(0,1x)+3*x^2*sin(1,2*x))) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  5                                   
  /                                   
 |                                    
 |  |         /x \      2    /6*x\|   
 |  |4 + 2*sin|--| + 3*x *sin|---|| dx
 |  |         \10/           \ 5 /|   
 |                                    
/                                     
1
∫15∣3x2sin⁡(6x5)+(2sin⁡(x10)+4)∣ dx\int\limits_{1}^{5} \left|{3 x^{2} \sin{\left(\frac{6 x}{5} \right)} + \left(2 \sin{\left(\frac{x}{10} \right)} + 4\right)}\right|\, dx 
Integral(Abs(4 + 2*sin(x/10) + (3*x^2)*sin(6*x/5)), (x, 1, 5))
Respuesta [src] 
  5                                                                           
  /                                                                           
 |                                                                            
 |  /         /x \      2    /6*x\                /x \      2    /6*x\        
 |  |4 + 2*sin|--| + 3*x *sin|---|   for 4 + 2*sin|--| + 3*x *sin|---| >= 0   
 |  |         \10/           \ 5 /                \10/           \ 5 /        
 |  <                                                                       dx
 |  |          /x \      2    /6*x\                                           
 |  |-4 - 2*sin|--| - 3*x *sin|---|                otherwise                  
 |  \          \10/           \ 5 /                                           
 |                                                                            
/                                                                             
1
∫15{3x2sin⁡(6x5)+2sin⁡(x10)+4for 3x2sin⁡(6x5)+2sin⁡(x10)+4≥0−3x2sin⁡(6x5)−2sin⁡(x10)−4otherwise dx\int\limits_{1}^{5} \begin{cases} 3 x^{2} \sin{\left(\frac{6 x}{5} \right)} + 2 \sin{\left(\frac{x}{10} \right)} + 4 & \text{for}\: 3 x^{2} \sin{\left(\frac{6 x}{5} \right)} + 2 \sin{\left(\frac{x}{10} \right)} + 4 \geq 0 \\- 3 x^{2} \sin{\left(\frac{6 x}{5} \right)} - 2 \sin{\left(\frac{x}{10} \right)} - 4 & \text{otherwise} \end{cases}\, dx 
=
= 
  5                                                                           
  /                                                                           
 |                                                                            
 |  /         /x \      2    /6*x\                /x \      2    /6*x\        
 |  |4 + 2*sin|--| + 3*x *sin|---|   for 4 + 2*sin|--| + 3*x *sin|---| >= 0   
 |  |         \10/           \ 5 /                \10/           \ 5 /        
 |  <                                                                       dx
 |  |          /x \      2    /6*x\                                           
 |  |-4 - 2*sin|--| - 3*x *sin|---|                otherwise                  
 |  \          \10/           \ 5 /                                           
 |                                                                            
/                                                                             
1
∫15{3x2sin⁡(6x5)+2sin⁡(x10)+4for 3x2sin⁡(6x5)+2sin⁡(x10)+4≥0−3x2sin⁡(6x5)−2sin⁡(x10)−4otherwise dx\int\limits_{1}^{5} \begin{cases} 3 x^{2} \sin{\left(\frac{6 x}{5} \right)} + 2 \sin{\left(\frac{x}{10} \right)} + 4 & \text{for}\: 3 x^{2} \sin{\left(\frac{6 x}{5} \right)} + 2 \sin{\left(\frac{x}{10} \right)} + 4 \geq 0 \\- 3 x^{2} \sin{\left(\frac{6 x}{5} \right)} - 2 \sin{\left(\frac{x}{10} \right)} - 4 & \text{otherwise} \end{cases}\, dx 
Integral(Piecewise((4 + 2*sin(x/10) + 3*x^2*sin(6*x/5), 4 + 2*sin(x/10) + 3*x^2*sin(6*x/5) >= 0), (-4 - 2*sin(x/10) - 3*x^2*sin(6*x/5), True)), (x, 1, 5))
Respuesta numérica [src] 
82.1205096002632
82.1205096002632

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

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