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Resolución de integrales/ sin^2/ cos^6/ (2^8)(sin^2x)(cos^6x)

Integral de (2^8)(sin^2x)(cos^6x) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
   0                       
   /                       
  |                        
  |         2       6      
  |  256*sin (x)*cos (x) dx
  |                        
 /                         
-pi                        
----                       
 2
∫−π20256sin⁡2(x)cos⁡6(x) dx\int\limits_{- \frac{\pi}{2}}^{0} 256 \sin^{2}{\left(x \right)} \cos^{6}{\left(x \right)}\, dx 
Integral((256*sin(x)^2)*cos(x)^6, (x, -pi/2, 0))
Respuesta (Indefinida) [src] 
  /                                                                                                                                                                                                                 
 |                                                                                                           3       5             5       3                                                                        
 |        2       6                   7                     8              8            7             110*cos (x)*sin (x)   146*cos (x)*sin (x)           2       6              6       2              4       4   
 | 256*sin (x)*cos (x) dx = C - 10*cos (x)*sin(x) + 10*x*cos (x) + 10*x*sin (x) + 10*sin (x)*cos(x) + ------------------- + ------------------- + 40*x*cos (x)*sin (x) + 40*x*cos (x)*sin (x) + 60*x*cos (x)*sin (x)
 |                                                                                                             3                     3                                                                              
/
∫256sin⁡2(x)cos⁡6(x) dx=C+10xsin⁡8(x)+40xsin⁡6(x)cos⁡2(x)+60xsin⁡4(x)cos⁡4(x)+40xsin⁡2(x)cos⁡6(x)+10xcos⁡8(x)+10sin⁡7(x)cos⁡(x)+110sin⁡5(x)cos⁡3(x)3+146sin⁡3(x)cos⁡5(x)3−10sin⁡(x)cos⁡7(x)\int 256 \sin^{2}{\left(x \right)} \cos^{6}{\left(x \right)}\, dx = C + 10 x \sin^{8}{\left(x \right)} + 40 x \sin^{6}{\left(x \right)} \cos^{2}{\left(x \right)} + 60 x \sin^{4}{\left(x \right)} \cos^{4}{\left(x \right)} + 40 x \sin^{2}{\left(x \right)} \cos^{6}{\left(x \right)} + 10 x \cos^{8}{\left(x \right)} + 10 \sin^{7}{\left(x \right)} \cos{\left(x \right)} + \frac{110 \sin^{5}{\left(x \right)} \cos^{3}{\left(x \right)}}{3} + \frac{146 \sin^{3}{\left(x \right)} \cos^{5}{\left(x \right)}}{3} - 10 \sin{\left(x \right)} \cos^{7}{\left(x \right)}
Simplificar
Gráfica
-1.5-1.4-1.3-1.2-1.1-1.0-0.9-0.8-0.7-0.6-0.5-0.4-0.3-0.2-0.10.0-5050
Trazar el gráfico f(x)
Respuesta [src] 
5*pi
5π5 \pi 
=
= 
5*pi
5π5 \pi 
5*pi
Respuesta numérica [src] 
15.707963267949
15.707963267949

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

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