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Resolución de integrales/ sin^4/ cos^4/ 16sin^4(x)cos^4(x)

Integral de 16sin^4(x)cos^4(x) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                      
  /                      
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 |        4       4      
 |  16*sin (x)*cos (x) dx
 |                       
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0
∫0116sin⁡4(x)cos⁡4(x) dx\int\limits_{0}^{1} 16 \sin^{4}{\left(x \right)} \cos^{4}{\left(x \right)}\, dx 
Integral((16*sin(x)^4)*cos(x)^4, (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                                                                                                                                                                                                       
 |                                   5       3           7                    8             8           7                   3       5             2       6             6       2             4       4   
 |       4       4             11*cos (x)*sin (x)   3*cos (x)*sin(x)   3*x*cos (x)   3*x*sin (x)   3*sin (x)*cos(x)   11*cos (x)*sin (x)   3*x*cos (x)*sin (x)   3*x*cos (x)*sin (x)   9*x*cos (x)*sin (x)
 | 16*sin (x)*cos (x) dx = C - ------------------ - ---------------- + ----------- + ----------- + ---------------- + ------------------ + ------------------- + ------------------- + -------------------
 |                                     8                   8                8             8               8                   8                     2                     2                     4         
/
∫16sin⁡4(x)cos⁡4(x) dx=C+3xsin⁡8(x)8+3xsin⁡6(x)cos⁡2(x)2+9xsin⁡4(x)cos⁡4(x)4+3xsin⁡2(x)cos⁡6(x)2+3xcos⁡8(x)8+3sin⁡7(x)cos⁡(x)8+11sin⁡5(x)cos⁡3(x)8−11sin⁡3(x)cos⁡5(x)8−3sin⁡(x)cos⁡7(x)8\int 16 \sin^{4}{\left(x \right)} \cos^{4}{\left(x \right)}\, dx = C + \frac{3 x \sin^{8}{\left(x \right)}}{8} + \frac{3 x \sin^{6}{\left(x \right)} \cos^{2}{\left(x \right)}}{2} + \frac{9 x \sin^{4}{\left(x \right)} \cos^{4}{\left(x \right)}}{4} + \frac{3 x \sin^{2}{\left(x \right)} \cos^{6}{\left(x \right)}}{2} + \frac{3 x \cos^{8}{\left(x \right)}}{8} + \frac{3 \sin^{7}{\left(x \right)} \cos{\left(x \right)}}{8} + \frac{11 \sin^{5}{\left(x \right)} \cos^{3}{\left(x \right)}}{8} - \frac{11 \sin^{3}{\left(x \right)} \cos^{5}{\left(x \right)}}{8} - \frac{3 \sin{\left(x \right)} \cos^{7}{\left(x \right)}}{8}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.9002
Trazar el gráfico f(x)
Respuesta [src] 
                         3          
3   3*cos(2)*sin(2)   sin (2)*cos(2)
- - --------------- - --------------
8          16               8
−sin⁡3(2)cos⁡(2)8−3sin⁡(2)cos⁡(2)16+38- \frac{\sin^{3}{\left(2 \right)} \cos{\left(2 \right)}}{8} - \frac{3 \sin{\left(2 \right)} \cos{\left(2 \right)}}{16} + \frac{3}{8} 
=
= 
                         3          
3   3*cos(2)*sin(2)   sin (2)*cos(2)
- - --------------- - --------------
8          16               8
−sin⁡3(2)cos⁡(2)8−3sin⁡(2)cos⁡(2)16+38- \frac{\sin^{3}{\left(2 \right)} \cos{\left(2 \right)}}{8} - \frac{3 \sin{\left(2 \right)} \cos{\left(2 \right)}}{16} + \frac{3}{8} 
3/8 - 3*cos(2)*sin(2)/16 - sin(2)^3*cos(2)/8
Respuesta numérica [src] 
0.485059034516981
0.485059034516981

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

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