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Resolución de integrales/ sin(y)/ (-y^2*sin(y)^3)

Integral de (-y^2*sin(y)^3) dy

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  y               
  /               
 |                
 |    2    3      
 |  -y *sin (y) dy
 |                
/                 
1
$$\int\limits_{1}^{y} - y^{2} \sin^{3}{\left(y \right)}\, dy$$ 
Integral((-y^2)*sin(y)^3, (y, 1, y))
Respuesta (Indefinida) [src] 
  /                                                                                                                          
 |                            3              3            2                2    3                                 2          
 |   2    3             40*cos (y)   14*y*sin (y)   14*sin (y)*cos(y)   2*y *cos (y)    2    2             4*y*cos (y)*sin(y)
 | -y *sin (y) dy = C - ---------- - ------------ - ----------------- + ------------ + y *sin (y)*cos(y) - ------------------
 |                          27            9                 9                3                                     3         
/
$$\int - y^{2} \sin^{3}{\left(y \right)}\, dy = C + y^{2} \sin^{2}{\left(y \right)} \cos{\left(y \right)} + \frac{2 y^{2} \cos^{3}{\left(y \right)}}{3} - \frac{14 y \sin^{3}{\left(y \right)}}{9} - \frac{4 y \sin{\left(y \right)} \cos^{2}{\left(y \right)}}{3} - \frac{14 \sin^{2}{\left(y \right)} \cos{\left(y \right)}}{9} - \frac{40 \cos^{3}{\left(y \right)}}{27}$$
Simplificar
Respuesta [src] 
        3            3            3              3            2                2    3           2                  2                                        2          
  40*cos (y)   14*sin (1)   22*cos (1)   14*y*sin (y)   14*sin (y)*cos(y)   2*y *cos (y)   4*cos (1)*sin(1)   5*sin (1)*cos(1)    2    2             4*y*cos (y)*sin(y)
- ---------- + ---------- + ---------- - ------------ - ----------------- + ------------ + ---------------- + ---------------- + y *sin (y)*cos(y) - ------------------
      27           9            27            9                 9                3                3                  9                                       3
$$y^{2} \sin^{2}{\left(y \right)} \cos{\left(y \right)} + \frac{2 y^{2} \cos^{3}{\left(y \right)}}{3} - \frac{14 y \sin^{3}{\left(y \right)}}{9} - \frac{4 y \sin{\left(y \right)} \cos^{2}{\left(y \right)}}{3} - \frac{14 \sin^{2}{\left(y \right)} \cos{\left(y \right)}}{9} - \frac{40 \cos^{3}{\left(y \right)}}{27} + \frac{22 \cos^{3}{\left(1 \right)}}{27} + \frac{5 \sin^{2}{\left(1 \right)} \cos{\left(1 \right)}}{9} + \frac{4 \sin{\left(1 \right)} \cos^{2}{\left(1 \right)}}{3} + \frac{14 \sin^{3}{\left(1 \right)}}{9}$$ 
=
= 
        3            3            3              3            2                2    3           2                  2                                        2          
  40*cos (y)   14*sin (1)   22*cos (1)   14*y*sin (y)   14*sin (y)*cos(y)   2*y *cos (y)   4*cos (1)*sin(1)   5*sin (1)*cos(1)    2    2             4*y*cos (y)*sin(y)
- ---------- + ---------- + ---------- - ------------ - ----------------- + ------------ + ---------------- + ---------------- + y *sin (y)*cos(y) - ------------------
      27           9            27            9                 9                3                3                  9                                       3
$$y^{2} \sin^{2}{\left(y \right)} \cos{\left(y \right)} + \frac{2 y^{2} \cos^{3}{\left(y \right)}}{3} - \frac{14 y \sin^{3}{\left(y \right)}}{9} - \frac{4 y \sin{\left(y \right)} \cos^{2}{\left(y \right)}}{3} - \frac{14 \sin^{2}{\left(y \right)} \cos{\left(y \right)}}{9} - \frac{40 \cos^{3}{\left(y \right)}}{27} + \frac{22 \cos^{3}{\left(1 \right)}}{27} + \frac{5 \sin^{2}{\left(1 \right)} \cos{\left(1 \right)}}{9} + \frac{4 \sin{\left(1 \right)} \cos^{2}{\left(1 \right)}}{3} + \frac{14 \sin^{3}{\left(1 \right)}}{9}$$ 
-40*cos(y)^3/27 + 14*sin(1)^3/9 + 22*cos(1)^3/27 - 14*y*sin(y)^3/9 - 14*sin(y)^2*cos(y)/9 + 2*y^2*cos(y)^3/3 + 4*cos(1)^2*sin(1)/3 + 5*sin(1)^2*cos(1)/9 + y^2*sin(y)^2*cos(y) - 4*y*cos(y)^2*sin(y)/3

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

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