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Resolución de integrales/ cos(t)/ sin(t)/ cos(t)^2*sin(t)^2*t

Integral de cos(t)^2*sin(t)^2*t dt

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                     
  /                     
 |                      
 |     2       2        
 |  cos (t)*sin (t)*t dt
 |                      
/                       
0
$$\int\limits_{0}^{1} t \sin^{2}{\left(t \right)} \cos^{2}{\left(t \right)}\, dt$$ 
Integral((cos(t)^2*sin(t)^2)*t, (t, 0, 1))
Respuesta (Indefinida) [src] 
  /                                                                                                                                 
 |                               4         4       2    4       2    4           3                  3              2    2       2   
 |    2       2               cos (t)   sin (t)   t *cos (t)   t *sin (t)   t*cos (t)*sin(t)   t*sin (t)*cos(t)   t *cos (t)*sin (t)
 | cos (t)*sin (t)*t dt = C - ------- - ------- + ---------- + ---------- - ---------------- + ---------------- + ------------------
 |                               32        32         16           16              8                  8                   8         
/
$$\int t \sin^{2}{\left(t \right)} \cos^{2}{\left(t \right)}\, dt = C + \frac{t^{2} \sin^{4}{\left(t \right)}}{16} + \frac{t^{2} \sin^{2}{\left(t \right)} \cos^{2}{\left(t \right)}}{8} + \frac{t^{2} \cos^{4}{\left(t \right)}}{16} + \frac{t \sin^{3}{\left(t \right)} \cos{\left(t \right)}}{8} - \frac{t \sin{\left(t \right)} \cos^{3}{\left(t \right)}}{8} - \frac{\sin^{4}{\left(t \right)}}{32} - \frac{\cos^{4}{\left(t \right)}}{32}$$
Simplificar
Gráfica
Trazar el gráfico f(x)
Respuesta [src] 
        4         4         3                2       2         3          
1    cos (1)   sin (1)   cos (1)*sin(1)   cos (1)*sin (1)   sin (1)*cos(1)
-- + ------- + ------- - -------------- + --------------- + --------------
32      32        32           8                 8                8
$$- \frac{\sin{\left(1 \right)} \cos^{3}{\left(1 \right)}}{8} + \frac{\cos^{4}{\left(1 \right)}}{32} + \frac{\sin^{4}{\left(1 \right)}}{32} + \frac{\sin^{2}{\left(1 \right)} \cos^{2}{\left(1 \right)}}{8} + \frac{1}{32} + \frac{\sin^{3}{\left(1 \right)} \cos{\left(1 \right)}}{8}$$ 
=
= 
        4         4         3                2       2         3          
1    cos (1)   sin (1)   cos (1)*sin(1)   cos (1)*sin (1)   sin (1)*cos(1)
-- + ------- + ------- - -------------- + --------------- + --------------
32      32        32           8                 8                8
$$- \frac{\sin{\left(1 \right)} \cos^{3}{\left(1 \right)}}{8} + \frac{\cos^{4}{\left(1 \right)}}{32} + \frac{\sin^{4}{\left(1 \right)}}{32} + \frac{\sin^{2}{\left(1 \right)} \cos^{2}{\left(1 \right)}}{8} + \frac{1}{32} + \frac{\sin^{3}{\left(1 \right)} \cos{\left(1 \right)}}{8}$$ 
1/32 + cos(1)^4/32 + sin(1)^4/32 - cos(1)^3*sin(1)/8 + cos(1)^2*sin(1)^2/8 + sin(1)^3*cos(1)/8
Respuesta numérica [src] 
0.0990691687663697
0.0990691687663697

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

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