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Integral de sin(30x+1)^5(cos(30x+1)^2) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src]
  1                                 
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 |                                  
 |     5              2             
 |  sin (30*x + 1)*cos (30*x + 1) dx
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0                                   
$$\int\limits_{0}^{1} \sin^{5}{\left(30 x + 1 \right)} \cos^{2}{\left(30 x + 1 \right)}\, dx$$
Integral(sin(30*x + 1)^5*cos(30*x + 1)^2, (x, 0, 1))
Gráfica
Respuesta [src]
       7            7           5        2          3        4          3       4           5       2   
  4*cos (31)   4*cos (1)   2*cos (31)*sin (31)   cos (31)*sin (31)   cos (1)*sin (1)   2*cos (1)*sin (1)
- ---------- + --------- - ------------------- - ----------------- + --------------- + -----------------
     1575         1575             225                   90                 90                225       
$$- \frac{4 \cos^{7}{\left(31 \right)}}{1575} - \frac{2 \sin^{2}{\left(31 \right)} \cos^{5}{\left(31 \right)}}{225} - \frac{\sin^{4}{\left(31 \right)} \cos^{3}{\left(31 \right)}}{90} + \frac{4 \cos^{7}{\left(1 \right)}}{1575} + \frac{2 \sin^{2}{\left(1 \right)} \cos^{5}{\left(1 \right)}}{225} + \frac{\sin^{4}{\left(1 \right)} \cos^{3}{\left(1 \right)}}{90}$$
=
=
       7            7           5        2          3        4          3       4           5       2   
  4*cos (31)   4*cos (1)   2*cos (31)*sin (31)   cos (31)*sin (31)   cos (1)*sin (1)   2*cos (1)*sin (1)
- ---------- + --------- - ------------------- - ----------------- + --------------- + -----------------
     1575         1575             225                   90                 90                225       
$$- \frac{4 \cos^{7}{\left(31 \right)}}{1575} - \frac{2 \sin^{2}{\left(31 \right)} \cos^{5}{\left(31 \right)}}{225} - \frac{\sin^{4}{\left(31 \right)} \cos^{3}{\left(31 \right)}}{90} + \frac{4 \cos^{7}{\left(1 \right)}}{1575} + \frac{2 \sin^{2}{\left(1 \right)} \cos^{5}{\left(1 \right)}}{225} + \frac{\sin^{4}{\left(1 \right)} \cos^{3}{\left(1 \right)}}{90}$$
-4*cos(31)^7/1575 + 4*cos(1)^7/1575 - 2*cos(31)^5*sin(31)^2/225 - cos(31)^3*sin(31)^4/90 + cos(1)^3*sin(1)^4/90 + 2*cos(1)^5*sin(1)^2/225
Respuesta numérica [src]
-0.00131443198331184
-0.00131443198331184

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