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Integral de 16sinx^6cosx^2 dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src]
  1                      
  /                      
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 |        6       2      
 |  16*sin (x)*cos (x) dx
 |                       
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0                        
$$\int\limits_{0}^{1} 16 \sin^{6}{\left(x \right)} \cos^{2}{\left(x \right)}\, dx$$
Integral((16*sin(x)^6)*cos(x)^2, (x, 0, 1))
Respuesta (Indefinida) [src]
  /                                                                                                                                                                                                        
 |                                   3       5            5       3           7                    8             8           7                    2       6             6       2              4       4   
 |       6       2             73*cos (x)*sin (x)   55*cos (x)*sin (x)   5*cos (x)*sin(x)   5*x*cos (x)   5*x*sin (x)   5*sin (x)*cos(x)   5*x*cos (x)*sin (x)   5*x*cos (x)*sin (x)   15*x*cos (x)*sin (x)
 | 16*sin (x)*cos (x) dx = C - ------------------ - ------------------ - ---------------- + ----------- + ----------- + ---------------- + ------------------- + ------------------- + --------------------
 |                                     24                   24                  8                8             8               8                    2                     2                     4          
/                                                                                                                                                                                                          
$$\int 16 \sin^{6}{\left(x \right)} \cos^{2}{\left(x \right)}\, dx = C + \frac{5 x \sin^{8}{\left(x \right)}}{8} + \frac{5 x \sin^{6}{\left(x \right)} \cos^{2}{\left(x \right)}}{2} + \frac{15 x \sin^{4}{\left(x \right)} \cos^{4}{\left(x \right)}}{4} + \frac{5 x \sin^{2}{\left(x \right)} \cos^{6}{\left(x \right)}}{2} + \frac{5 x \cos^{8}{\left(x \right)}}{8} + \frac{5 \sin^{7}{\left(x \right)} \cos{\left(x \right)}}{8} - \frac{73 \sin^{5}{\left(x \right)} \cos^{3}{\left(x \right)}}{24} - \frac{55 \sin^{3}{\left(x \right)} \cos^{5}{\left(x \right)}}{24} - \frac{5 \sin{\left(x \right)} \cos^{7}{\left(x \right)}}{8}$$
Gráfica
Respuesta [src]
                                              3                5          
5        7             5*cos(1)*sin(1)   5*sin (1)*cos(1)   sin (1)*cos(1)
- + 2*sin (1)*cos(1) - --------------- - ---------------- - --------------
8                             8                 12                3       
$$- \frac{5 \sin{\left(1 \right)} \cos{\left(1 \right)}}{8} - \frac{5 \sin^{3}{\left(1 \right)} \cos{\left(1 \right)}}{12} - \frac{\sin^{5}{\left(1 \right)} \cos{\left(1 \right)}}{3} + 2 \sin^{7}{\left(1 \right)} \cos{\left(1 \right)} + \frac{5}{8}$$
=
=
                                              3                5          
5        7             5*cos(1)*sin(1)   5*sin (1)*cos(1)   sin (1)*cos(1)
- + 2*sin (1)*cos(1) - --------------- - ---------------- - --------------
8                             8                 12                3       
$$- \frac{5 \sin{\left(1 \right)} \cos{\left(1 \right)}}{8} - \frac{5 \sin^{3}{\left(1 \right)} \cos{\left(1 \right)}}{12} - \frac{\sin^{5}{\left(1 \right)} \cos{\left(1 \right)}}{3} + 2 \sin^{7}{\left(1 \right)} \cos{\left(1 \right)} + \frac{5}{8}$$
5/8 + 2*sin(1)^7*cos(1) - 5*cos(1)*sin(1)/8 - 5*sin(1)^3*cos(1)/12 - sin(1)^5*cos(1)/3
Respuesta numérica [src]
0.45353260775367
0.45353260775367

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