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Resolución de integrales/ sqrt(C-B)(B-A)CA

Integral de sqrt(C-B)(B-A)CA dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                        
  /                        
 |                         
 |    _______          a   
 |  \/ c - b *(b - a)*c  dc
 |                         
/                          
0
∫01ca(−a+b)−b+c dc\int\limits_{0}^{1} c^{a} \left(- a + b\right) \sqrt{- b + c}\, dc 
Integral((sqrt(c - b)*(b - a))*c^a, (c, 0, 1))
Respuesta (Indefinida) [src] 
                                                                                                                                    
                                                     _  /        |          pi*I\                       _  /        |          pi*I\
  /                                   a        3/2  |_  |3/2, -a | (c - b)*e    |        a        3/2  |_  |3/2, -a | (c - b)*e    |
 |                               2*a*b *(c - b)   * |   |        | -------------|   2*b*b *(c - b)   * |   |        | -------------|
 |   _______          a                            2  1 \  5/2   |       b      /                     2  1 \  5/2   |       b      /
 | \/ c - b *(b - a)*c  dc = C - ------------------------------------------------ + ------------------------------------------------
 |                                                      3                                                  3                        
/
∫ca(−a+b)−b+c dc=C−2aba(−b+c)322F1(32,−a52|(−b+c)eiπb)3+2bba(−b+c)322F1(32,−a52|(−b+c)eiπb)3\int c^{a} \left(- a + b\right) \sqrt{- b + c}\, dc = C - \frac{2 a b^{a} \left(- b + c\right)^{\frac{3}{2}} {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, - a \\ \frac{5}{2} \end{matrix}\middle| {\frac{\left(- b + c\right) e^{i \pi}}{b}} \right)}}{3} + \frac{2 b b^{a} \left(- b + c\right)^{\frac{3}{2}} {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, - a \\ \frac{5}{2} \end{matrix}\middle| {\frac{\left(- b + c\right) e^{i \pi}}{b}} \right)}}{3}
Simplificar
Respuesta [src] 
                                                                                                  
                         _                                            _  /        |          pi*I\
     a     3/2          |_  /3/2, -a |  \      a        3/2          |_  |3/2, -a | (1 - b)*e    |
  2*b *(-b)   *(b - a)* |   |        | 1|   2*b *(1 - b)   *(b - a)* |   |        | -------------|
                       2  1 \  5/2   |  /                           2  1 \  5/2   |       b      /
- --------------------------------------- + ------------------------------------------------------
                     3                                                3
−2ba(−b)32(−a+b)2F1(32,−a52|1)3+2ba(1−b)32(−a+b)2F1(32,−a52|(1−b)eiπb)3- \frac{2 b^{a} \left(- b\right)^{\frac{3}{2}} \left(- a + b\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, - a \\ \frac{5}{2} \end{matrix}\middle| {1} \right)}}{3} + \frac{2 b^{a} \left(1 - b\right)^{\frac{3}{2}} \left(- a + b\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, - a \\ \frac{5}{2} \end{matrix}\middle| {\frac{\left(1 - b\right) e^{i \pi}}{b}} \right)}}{3} 
=
= 
                                                                                                  
                         _                                            _  /        |          pi*I\
     a     3/2          |_  /3/2, -a |  \      a        3/2          |_  |3/2, -a | (1 - b)*e    |
  2*b *(-b)   *(b - a)* |   |        | 1|   2*b *(1 - b)   *(b - a)* |   |        | -------------|
                       2  1 \  5/2   |  /                           2  1 \  5/2   |       b      /
- --------------------------------------- + ------------------------------------------------------
                     3                                                3
−2ba(−b)32(−a+b)2F1(32,−a52|1)3+2ba(1−b)32(−a+b)2F1(32,−a52|(1−b)eiπb)3- \frac{2 b^{a} \left(- b\right)^{\frac{3}{2}} \left(- a + b\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, - a \\ \frac{5}{2} \end{matrix}\middle| {1} \right)}}{3} + \frac{2 b^{a} \left(1 - b\right)^{\frac{3}{2}} \left(- a + b\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, - a \\ \frac{5}{2} \end{matrix}\middle| {\frac{\left(1 - b\right) e^{i \pi}}{b}} \right)}}{3} 
-2*b^a*(-b)^(3/2)*(b - a)*hyper((3/2, -a), (5/2,), 1)/3 + 2*b^a*(1 - b)^(3/2)*(b - a)*hyper((3/2, -a), (5/2,), (1 - b)*exp_polar(pi*i)/b)/3

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

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