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Resolución de integrales/ absolute(50+6*x-0,006*t^2)

Integral de absolute(50+6*x-0,006*t^2) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
 1920                     
   /                      
  |                       
  |   |              2|   
  |   |           3*t |   
  |   |50 + 6*x - ----| dx
  |   |           500 |   
  |                       
 /                        
10083                     
-----                     
  10
∫10083101920∣−3t2500+(6x+50)∣ dx\int\limits_{\frac{10083}{10}}^{1920} \left|{- \frac{3 t^{2}}{500} + \left(6 x + 50\right)}\right|\, dx 
Integral(|50 + 6*x - 3*t^2/500|, (x, 10083/10, 1920))
Respuesta [src] 
                                                                                                                                                                                2                                                             2                                                                        
            /     |        2                                              \             /           |        2                                              \     /          2 \      /       2                                              \              /     |          2 \             /           |          2 \
     __1, 1 |1  3 | 25    t                                               |      __0, 2 |3, 1       | 25    t                                               |     |30499    t  |      |25    t                                               |       __1, 1 |1  3 | 5785    t  |      __0, 2 |3, 1       | 5785    t  |
- 6*/__     |     | -- - ---- + Min(1920, Max(10083/10, t**2/1000 - 22/3))| - 6*/__     |           | -- - ---- + Min(1920, Max(10083/10, t**2/1000 - 22/3))| - 3*|----- - ----|  + 3*|-- - ---- + Min(1920, Max(10083/10, t**2/1000 - 22/3))|  + 6*/__     |     | ---- - ----| + 6*/__     |           | ---- - ----|
    \_|2, 2 \2  0 | 3    1000                                             /     \_|2, 2 \      2, 0 | 3    1000                                             /     \  30    1000/      \3    1000                                             /      \_|2, 2 \2  0 |  3     1000/     \_|2, 2 \      2, 0 |  3     1000/
−3(3049930−t21000)2+3(−t21000+min⁡(1920,max⁡(1008310,t21000−223))+253)2+6G2,21,1(1320|57853−t21000)−6G2,21,1(1320|−t21000+min⁡(1920,max⁡(1008310,t21000−223))+253)+6G2,20,2(3,12,0|57853−t21000)−6G2,20,2(3,12,0|−t21000+min⁡(1920,max⁡(1008310,t21000−223))+253)- 3 \left(\frac{30499}{30} - \frac{t^{2}}{1000}\right)^{2} + 3 \left(- \frac{t^{2}}{1000} + \min\left(1920, \max\left(\frac{10083}{10}, \frac{t^{2}}{1000} - \frac{22}{3}\right)\right) + \frac{25}{3}\right)^{2} + 6 {G_{2, 2}^{1, 1}\left(\begin{matrix} 1 & 3 \\2 & 0 \end{matrix} \middle| {\frac{5785}{3} - \frac{t^{2}}{1000}} \right)} - 6 {G_{2, 2}^{1, 1}\left(\begin{matrix} 1 & 3 \\2 & 0 \end{matrix} \middle| {- \frac{t^{2}}{1000} + \min\left(1920, \max\left(\frac{10083}{10}, \frac{t^{2}}{1000} - \frac{22}{3}\right)\right) + \frac{25}{3}} \right)} + 6 {G_{2, 2}^{0, 2}\left(\begin{matrix} 3, 1 & \\ & 2, 0 \end{matrix} \middle| {\frac{5785}{3} - \frac{t^{2}}{1000}} \right)} - 6 {G_{2, 2}^{0, 2}\left(\begin{matrix} 3, 1 & \\ & 2, 0 \end{matrix} \middle| {- \frac{t^{2}}{1000} + \min\left(1920, \max\left(\frac{10083}{10}, \frac{t^{2}}{1000} - \frac{22}{3}\right)\right) + \frac{25}{3}} \right)} 
=
= 
                                                                                                                                                                                2                                                             2                                                                        
            /     |        2                                              \             /           |        2                                              \     /          2 \      /       2                                              \              /     |          2 \             /           |          2 \
     __1, 1 |1  3 | 25    t                                               |      __0, 2 |3, 1       | 25    t                                               |     |30499    t  |      |25    t                                               |       __1, 1 |1  3 | 5785    t  |      __0, 2 |3, 1       | 5785    t  |
- 6*/__     |     | -- - ---- + Min(1920, Max(10083/10, t**2/1000 - 22/3))| - 6*/__     |           | -- - ---- + Min(1920, Max(10083/10, t**2/1000 - 22/3))| - 3*|----- - ----|  + 3*|-- - ---- + Min(1920, Max(10083/10, t**2/1000 - 22/3))|  + 6*/__     |     | ---- - ----| + 6*/__     |           | ---- - ----|
    \_|2, 2 \2  0 | 3    1000                                             /     \_|2, 2 \      2, 0 | 3    1000                                             /     \  30    1000/      \3    1000                                             /      \_|2, 2 \2  0 |  3     1000/     \_|2, 2 \      2, 0 |  3     1000/
−3(3049930−t21000)2+3(−t21000+min⁡(1920,max⁡(1008310,t21000−223))+253)2+6G2,21,1(1320|57853−t21000)−6G2,21,1(1320|−t21000+min⁡(1920,max⁡(1008310,t21000−223))+253)+6G2,20,2(3,12,0|57853−t21000)−6G2,20,2(3,12,0|−t21000+min⁡(1920,max⁡(1008310,t21000−223))+253)- 3 \left(\frac{30499}{30} - \frac{t^{2}}{1000}\right)^{2} + 3 \left(- \frac{t^{2}}{1000} + \min\left(1920, \max\left(\frac{10083}{10}, \frac{t^{2}}{1000} - \frac{22}{3}\right)\right) + \frac{25}{3}\right)^{2} + 6 {G_{2, 2}^{1, 1}\left(\begin{matrix} 1 & 3 \\2 & 0 \end{matrix} \middle| {\frac{5785}{3} - \frac{t^{2}}{1000}} \right)} - 6 {G_{2, 2}^{1, 1}\left(\begin{matrix} 1 & 3 \\2 & 0 \end{matrix} \middle| {- \frac{t^{2}}{1000} + \min\left(1920, \max\left(\frac{10083}{10}, \frac{t^{2}}{1000} - \frac{22}{3}\right)\right) + \frac{25}{3}} \right)} + 6 {G_{2, 2}^{0, 2}\left(\begin{matrix} 3, 1 & \\ & 2, 0 \end{matrix} \middle| {\frac{5785}{3} - \frac{t^{2}}{1000}} \right)} - 6 {G_{2, 2}^{0, 2}\left(\begin{matrix} 3, 1 & \\ & 2, 0 \end{matrix} \middle| {- \frac{t^{2}}{1000} + \min\left(1920, \max\left(\frac{10083}{10}, \frac{t^{2}}{1000} - \frac{22}{3}\right)\right) + \frac{25}{3}} \right)} 
-6*meijerg(((1,), (3,)), ((2,), (0,)), 25/3 - t^2/1000 + Min(1920, Max(10083/10, -22/3 + t^2/1000))) - 6*meijerg(((3, 1), ()), ((), (2, 0)), 25/3 - t^2/1000 + Min(1920, Max(10083/10, -22/3 + t^2/1000))) - 3*(30499/30 - t^2/1000)^2 + 3*(25/3 - t^2/1000 + Min(1920, Max(10083/10, -22/3 + t^2/1000)))^2 + 6*meijerg(((1,), (3,)), ((2,), (0,)), 5785/3 - t^2/1000) + 6*meijerg(((3, 1), ()), ((), (2, 0)), 5785/3 - t^2/1000)

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

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