Sr Examen
Integral de absolute(50+6*x-0,006*t^2) dx
Solución
Ha introducido
[src]
1920 / | | | 2| | | 3*t | | |50 + 6*x - ----| dx | | 500 | | / 10083 ----- 10
$$\int\limits_{\frac{10083}{10}}^{1920} \left|{- \frac{3 t^{2}}{500} + \left(6 x + 50\right)}\right|\, dx$$
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/
$$- 3 \left(\frac{30499}{30} - \frac{t^{2}}{1000}\right)^{2} + 3 \left(- \frac{t^{2}}{1000} + \min\left(1920, \max\left(\frac{10083}{10}, \frac{t^{2}}{1000} - \frac{22}{3}\right)\right) + \frac{25}{3}\right)^{2} + 6 {G_{2, 2}^{1, 1}\left(\begin{matrix} 1 & 3 \\2 & 0 \end{matrix} \middle| {\frac{5785}{3} - \frac{t^{2}}{1000}} \right)} - 6 {G_{2, 2}^{1, 1}\left(\begin{matrix} 1 & 3 \\2 & 0 \end{matrix} \middle| {- \frac{t^{2}}{1000} + \min\left(1920, \max\left(\frac{10083}{10}, \frac{t^{2}}{1000} - \frac{22}{3}\right)\right) + \frac{25}{3}} \right)} + 6 {G_{2, 2}^{0, 2}\left(\begin{matrix} 3, 1 & \\ & 2, 0 \end{matrix} \middle| {\frac{5785}{3} - \frac{t^{2}}{1000}} \right)} - 6 {G_{2, 2}^{0, 2}\left(\begin{matrix} 3, 1 & \\ & 2, 0 \end{matrix} \middle| {- \frac{t^{2}}{1000} + \min\left(1920, \max\left(\frac{10083}{10}, \frac{t^{2}}{1000} - \frac{22}{3}\right)\right) + \frac{25}{3}} \right)}$$
=
=
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/
$$- 3 \left(\frac{30499}{30} - \frac{t^{2}}{1000}\right)^{2} + 3 \left(- \frac{t^{2}}{1000} + \min\left(1920, \max\left(\frac{10083}{10}, \frac{t^{2}}{1000} - \frac{22}{3}\right)\right) + \frac{25}{3}\right)^{2} + 6 {G_{2, 2}^{1, 1}\left(\begin{matrix} 1 & 3 \\2 & 0 \end{matrix} \middle| {\frac{5785}{3} - \frac{t^{2}}{1000}} \right)} - 6 {G_{2, 2}^{1, 1}\left(\begin{matrix} 1 & 3 \\2 & 0 \end{matrix} \middle| {- \frac{t^{2}}{1000} + \min\left(1920, \max\left(\frac{10083}{10}, \frac{t^{2}}{1000} - \frac{22}{3}\right)\right) + \frac{25}{3}} \right)} + 6 {G_{2, 2}^{0, 2}\left(\begin{matrix} 3, 1 & \\ & 2, 0 \end{matrix} \middle| {\frac{5785}{3} - \frac{t^{2}}{1000}} \right)} - 6 {G_{2, 2}^{0, 2}\left(\begin{matrix} 3, 1 & \\ & 2, 0 \end{matrix} \middle| {- \frac{t^{2}}{1000} + \min\left(1920, \max\left(\frac{10083}{10}, \frac{t^{2}}{1000} - \frac{22}{3}\right)\right) + \frac{25}{3}} \right)}$$
-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.