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Integral de Cos^2(x-10p) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src]
 p                   
 --                  
 81                  
  /                  
 |                   
 |     2             
 |  cos (x - 10*p) dx
 |                   
/                    
-p                   
---                  
 8                   
$$\int\limits_{- \frac{p}{8}}^{\frac{p}{81}} \cos^{2}{\left(- 10 p + x \right)}\, dx$$
Integral(cos(x - 10*p)^2, (x, -p/8, p/81))
Respuesta [src]
   /81*p\    /81*p\      /809*p\    /809*p\        2/81*p\        2/81*p\        2/809*p\        2/809*p\
cos|----|*sin|----|   cos|-----|*sin|-----|   p*cos |----|   p*sin |----|   p*cos |-----|   p*sin |-----|
   \ 8  /    \ 8  /      \  81 /    \  81 /         \ 8  /         \ 8  /         \  81 /         \  81 /
------------------- - --------------------- + ------------ + ------------ + ------------- + -------------
         2                      2                  16             16             162             162     
$$\frac{p \sin^{2}{\left(\frac{809 p}{81} \right)}}{162} + \frac{p \sin^{2}{\left(\frac{81 p}{8} \right)}}{16} + \frac{p \cos^{2}{\left(\frac{809 p}{81} \right)}}{162} + \frac{p \cos^{2}{\left(\frac{81 p}{8} \right)}}{16} - \frac{\sin{\left(\frac{809 p}{81} \right)} \cos{\left(\frac{809 p}{81} \right)}}{2} + \frac{\sin{\left(\frac{81 p}{8} \right)} \cos{\left(\frac{81 p}{8} \right)}}{2}$$
=
=
   /81*p\    /81*p\      /809*p\    /809*p\        2/81*p\        2/81*p\        2/809*p\        2/809*p\
cos|----|*sin|----|   cos|-----|*sin|-----|   p*cos |----|   p*sin |----|   p*cos |-----|   p*sin |-----|
   \ 8  /    \ 8  /      \  81 /    \  81 /         \ 8  /         \ 8  /         \  81 /         \  81 /
------------------- - --------------------- + ------------ + ------------ + ------------- + -------------
         2                      2                  16             16             162             162     
$$\frac{p \sin^{2}{\left(\frac{809 p}{81} \right)}}{162} + \frac{p \sin^{2}{\left(\frac{81 p}{8} \right)}}{16} + \frac{p \cos^{2}{\left(\frac{809 p}{81} \right)}}{162} + \frac{p \cos^{2}{\left(\frac{81 p}{8} \right)}}{16} - \frac{\sin{\left(\frac{809 p}{81} \right)} \cos{\left(\frac{809 p}{81} \right)}}{2} + \frac{\sin{\left(\frac{81 p}{8} \right)} \cos{\left(\frac{81 p}{8} \right)}}{2}$$
cos(81*p/8)*sin(81*p/8)/2 - cos(809*p/81)*sin(809*p/81)/2 + p*cos(81*p/8)^2/16 + p*sin(81*p/8)^2/16 + p*cos(809*p/81)^2/162 + p*sin(809*p/81)^2/162

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