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Resolución de integrales/ cos(t)/ sin(t)/ b*cos(t)^2*(-3b)*sin(t)^4

Integral de b*cos(t)^2*(-3b)*sin(t)^4 dt

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  0                          
  /                          
 |                           
 |       2            4      
 |  b*cos (t)*-3*b*sin (t) dt
 |                           
/                            
pi                           
--                           
2
∫π20−3bbcos⁡2(t)sin⁡4(t) dt\int\limits_{\frac{\pi}{2}}^{0} - 3 b b \cos^{2}{\left(t \right)} \sin^{4}{\left(t \right)}\, dt 
Integral(((b*cos(t)^2)*(-3*b))*sin(t)^4, (t, pi/2, 0))
Respuesta (Indefinida) [src] 
  /                                                                                                                                                              
 |                                      /     3       3         5                  6           6         5                    2       4             4       2   \
 |      2            4                2 |  cos (t)*sin (t)   cos (t)*sin(t)   t*cos (t)   t*sin (t)   sin (t)*cos(t)   3*t*cos (t)*sin (t)   3*t*cos (t)*sin (t)|
 | b*cos (t)*-3*b*sin (t) dt = C - 3*b *|- --------------- - -------------- + --------- + --------- + -------------- + ------------------- + -------------------|
 |                                      \         6                16             16          16            16                  16                    16        /
/
∫−3bbcos⁡2(t)sin⁡4(t) dt=C−3b2(tsin⁡6(t)16+3tsin⁡4(t)cos⁡2(t)16+3tsin⁡2(t)cos⁡4(t)16+tcos⁡6(t)16+sin⁡5(t)cos⁡(t)16−sin⁡3(t)cos⁡3(t)6−sin⁡(t)cos⁡5(t)16)\int - 3 b b \cos^{2}{\left(t \right)} \sin^{4}{\left(t \right)}\, dt = C - 3 b^{2} \left(\frac{t \sin^{6}{\left(t \right)}}{16} + \frac{3 t \sin^{4}{\left(t \right)} \cos^{2}{\left(t \right)}}{16} + \frac{3 t \sin^{2}{\left(t \right)} \cos^{4}{\left(t \right)}}{16} + \frac{t \cos^{6}{\left(t \right)}}{16} + \frac{\sin^{5}{\left(t \right)} \cos{\left(t \right)}}{16} - \frac{\sin^{3}{\left(t \right)} \cos^{3}{\left(t \right)}}{6} - \frac{\sin{\left(t \right)} \cos^{5}{\left(t \right)}}{16}\right)
Simplificar
Respuesta [src] 
      2
3*pi*b 
-------
   32
3πb232\frac{3 \pi b^{2}}{32} 
=
= 
      2
3*pi*b 
-------
   32
3πb232\frac{3 \pi b^{2}}{32} 
3*pi*b^2/32

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

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