Sr Examen

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Resolución de integrales/ |x-y|

Integral de |x-y| dy

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1           
  /           
 |            
 |  |x - y| dy
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/             
0
∫01∣x−y∣ dy\int\limits_{0}^{1} \left|{x - y}\right|\, dy 
Integral(|x - y|, (y, 0, 1))
Respuesta [src] 
                            2                                                                                                      2                                                        
(-x + Min(1, Max(0, x + 1)))     __1, 1 /1  3 |                           \    __0, 2 /3, 1       |                           \   x     __1, 1 /1  3 |      \    __0, 2 /3, 1       |      \
----------------------------- - /__     |     | -x + Min(1, Max(0, x + 1))| - /__     |           | -x + Min(1, Max(0, x + 1))| - -- + /__     |     | 1 - x| + /__     |           | 1 - x|
              2                 \_|2, 2 \2  0 |                           /   \_|2, 2 \      2, 0 |                           /   2    \_|2, 2 \2  0 |      /   \_|2, 2 \      2, 0 |      /
−x22+(−x+min⁡(1,max⁡(0,x+1)))22+G2,21,1(1320|1−x)−G2,21,1(1320|−x+min⁡(1,max⁡(0,x+1)))+G2,20,2(3,12,0|1−x)−G2,20,2(3,12,0|−x+min⁡(1,max⁡(0,x+1)))- \frac{x^{2}}{2} + \frac{\left(- x + \min\left(1, \max\left(0, x + 1\right)\right)\right)^{2}}{2} + {G_{2, 2}^{1, 1}\left(\begin{matrix} 1 & 3 \\2 & 0 \end{matrix} \middle| {1 - x} \right)} - {G_{2, 2}^{1, 1}\left(\begin{matrix} 1 & 3 \\2 & 0 \end{matrix} \middle| {- x + \min\left(1, \max\left(0, x + 1\right)\right)} \right)} + {G_{2, 2}^{0, 2}\left(\begin{matrix} 3, 1 & \\ & 2, 0 \end{matrix} \middle| {1 - x} \right)} - {G_{2, 2}^{0, 2}\left(\begin{matrix} 3, 1 & \\ & 2, 0 \end{matrix} \middle| {- x + \min\left(1, \max\left(0, x + 1\right)\right)} \right)} 
=
= 
                            2                                                                                                      2                                                        
(-x + Min(1, Max(0, x + 1)))     __1, 1 /1  3 |                           \    __0, 2 /3, 1       |                           \   x     __1, 1 /1  3 |      \    __0, 2 /3, 1       |      \
----------------------------- - /__     |     | -x + Min(1, Max(0, x + 1))| - /__     |           | -x + Min(1, Max(0, x + 1))| - -- + /__     |     | 1 - x| + /__     |           | 1 - x|
              2                 \_|2, 2 \2  0 |                           /   \_|2, 2 \      2, 0 |                           /   2    \_|2, 2 \2  0 |      /   \_|2, 2 \      2, 0 |      /
−x22+(−x+min⁡(1,max⁡(0,x+1)))22+G2,21,1(1320|1−x)−G2,21,1(1320|−x+min⁡(1,max⁡(0,x+1)))+G2,20,2(3,12,0|1−x)−G2,20,2(3,12,0|−x+min⁡(1,max⁡(0,x+1)))- \frac{x^{2}}{2} + \frac{\left(- x + \min\left(1, \max\left(0, x + 1\right)\right)\right)^{2}}{2} + {G_{2, 2}^{1, 1}\left(\begin{matrix} 1 & 3 \\2 & 0 \end{matrix} \middle| {1 - x} \right)} - {G_{2, 2}^{1, 1}\left(\begin{matrix} 1 & 3 \\2 & 0 \end{matrix} \middle| {- x + \min\left(1, \max\left(0, x + 1\right)\right)} \right)} + {G_{2, 2}^{0, 2}\left(\begin{matrix} 3, 1 & \\ & 2, 0 \end{matrix} \middle| {1 - x} \right)} - {G_{2, 2}^{0, 2}\left(\begin{matrix} 3, 1 & \\ & 2, 0 \end{matrix} \middle| {- x + \min\left(1, \max\left(0, x + 1\right)\right)} \right)} 
(-x + Min(1, Max(0, 1 + x)))^2/2 - meijerg(((1,), (3,)), ((2,), (0,)), -x + Min(1, Max(0, 1 + x))) - meijerg(((3, 1), ()), ((), (2, 0)), -x + Min(1, Max(0, 1 + x))) - x^2/2 + meijerg(((1,), (3,)), ((2,), (0,)), 1 - x) + meijerg(((3, 1), ()), ((), (2, 0)), 1 - x)

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

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