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Resolución de integrales/ 16*a^4*cos^4(x)*(((sin^2(x))/4)+((cos^2(x))/4))

Integral de 16*a^4*cos^4(x)*(((sin^2(x))/4)+((cos^2(x))/4)) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  2                                     
  /                                     
 |                                      
 |                /   2         2   \   
 |      4    4    |sin (x)   cos (x)|   
 |  16*a *cos (x)*|------- + -------| dx
 |                \   4         4   /   
 |                                      
/                                       
0
$$\int\limits_{0}^{2} 16 a^{4} \cos^{4}{\left(x \right)} \left(\frac{\sin^{2}{\left(x \right)}}{4} + \frac{\cos^{2}{\left(x \right)}}{4}\right)\, dx$$ 
Integral(((16*a^4)*cos(x)^4)*(sin(x)^2/4 + cos(x)^2/4), (x, 0, 2))
Respuesta [src] 
      /     6           6         3       3           5                  5                  2       4           4       2   \
    4 |3*cos (2)   3*sin (2)   cos (2)*sin (2)   3*sin (2)*cos(2)   5*cos (2)*sin(2)   9*cos (2)*sin (2)   9*cos (2)*sin (2)|
16*a *|--------- + --------- + --------------- + ---------------- + ---------------- + ----------------- + -----------------|
      \    16          16             4                 32                 32                  16                  16       /
$$16 a^{4} \left(\frac{3 \sin^{5}{\left(2 \right)} \cos{\left(2 \right)}}{32} + \frac{\sin^{3}{\left(2 \right)} \cos^{3}{\left(2 \right)}}{4} + \frac{5 \sin{\left(2 \right)} \cos^{5}{\left(2 \right)}}{32} + \frac{3 \cos^{6}{\left(2 \right)}}{16} + \frac{9 \sin^{2}{\left(2 \right)} \cos^{4}{\left(2 \right)}}{16} + \frac{9 \sin^{4}{\left(2 \right)} \cos^{2}{\left(2 \right)}}{16} + \frac{3 \sin^{6}{\left(2 \right)}}{16}\right)$$ 
=
= 
      /     6           6         3       3           5                  5                  2       4           4       2   \
    4 |3*cos (2)   3*sin (2)   cos (2)*sin (2)   3*sin (2)*cos(2)   5*cos (2)*sin(2)   9*cos (2)*sin (2)   9*cos (2)*sin (2)|
16*a *|--------- + --------- + --------------- + ---------------- + ---------------- + ----------------- + -----------------|
      \    16          16             4                 32                 32                  16                  16       /
$$16 a^{4} \left(\frac{3 \sin^{5}{\left(2 \right)} \cos{\left(2 \right)}}{32} + \frac{\sin^{3}{\left(2 \right)} \cos^{3}{\left(2 \right)}}{4} + \frac{5 \sin{\left(2 \right)} \cos^{5}{\left(2 \right)}}{32} + \frac{3 \cos^{6}{\left(2 \right)}}{16} + \frac{9 \sin^{2}{\left(2 \right)} \cos^{4}{\left(2 \right)}}{16} + \frac{9 \sin^{4}{\left(2 \right)} \cos^{2}{\left(2 \right)}}{16} + \frac{3 \sin^{6}{\left(2 \right)}}{16}\right)$$ 
16*a^4*(3*cos(2)^6/16 + 3*sin(2)^6/16 + cos(2)^3*sin(2)^3/4 + 3*sin(2)^5*cos(2)/32 + 5*cos(2)^5*sin(2)/32 + 9*cos(2)^2*sin(2)^4/16 + 9*cos(2)^4*sin(2)^2/16)

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

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