Sr Examen

Otras calculadoras

Resolución de integrales/ x*cos(n*π*x)

Integral de x*cos(n*π*x) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                 
  /                 
 |                  
 |  x*cos(n*pi*x) dx
 |                  
/                   
0
∫01xcos⁡(xπn) dx\int\limits_{0}^{1} x \cos{\left(x \pi n \right)}\, dx 
Integral(x*cos((n*pi)*x), (x, 0, 1))
Respuesta (Indefinida) [src] 
                          //              2                         \                              
                          ||             x                          |                              
                          ||             --                for n = 0|                              
                          ||             2                          |                              
  /                       ||                                        |     //     x       for n = 0\
 |                        ||/-cos(pi*n*x)                           |     ||                      |
 | x*cos(n*pi*x) dx = C - |<|-------------  for pi*n != 0           | + x*|
∫xcos⁡(xπn) dx=C+x({xfor n=0sin⁡(πnx)πnotherwise)−{x22for n=0{−cos⁡(πnx)πnfor πn≠00otherwiseπnotherwise\int x \cos{\left(x \pi n \right)}\, dx = C + x \left(\begin{cases} x & \text{for}\: n = 0 \\\frac{\sin{\left(\pi n x \right)}}{\pi n} & \text{otherwise} \end{cases}\right) - \begin{cases} \frac{x^{2}}{2} & \text{for}\: n = 0 \\\frac{\begin{cases} - \frac{\cos{\left(\pi n x \right)}}{\pi n} & \text{for}\: \pi n \neq 0 \\0 & \text{otherwise} \end{cases}}{\pi n} & \text{otherwise} \end{cases}
Simplificar
Respuesta [src] 
/    1      sin(pi*n)   cos(pi*n)                                  
|- ------ + --------- + ---------  for And(n > -oo, n < oo, n != 0)
|    2  2      pi*n         2  2                                   
<  pi *n                  pi *n                                    
|                                                                  
|              1/2                            otherwise            
\
{sin⁡(πn)πn+cos⁡(πn)π2n2−1π2n2for n>−∞∧n<∞∧n≠012otherwise\begin{cases} \frac{\sin{\left(\pi n \right)}}{\pi n} + \frac{\cos{\left(\pi n \right)}}{\pi^{2} n^{2}} - \frac{1}{\pi^{2} n^{2}} & \text{for}\: n > -\infty \wedge n < \infty \wedge n \neq 0 \\\frac{1}{2} & \text{otherwise} \end{cases} 
=
= 
/    1      sin(pi*n)   cos(pi*n)                                  
|- ------ + --------- + ---------  for And(n > -oo, n < oo, n != 0)
|    2  2      pi*n         2  2                                   
<  pi *n                  pi *n                                    
|                                                                  
|              1/2                            otherwise            
\
{sin⁡(πn)πn+cos⁡(πn)π2n2−1π2n2for n>−∞∧n<∞∧n≠012otherwise\begin{cases} \frac{\sin{\left(\pi n \right)}}{\pi n} + \frac{\cos{\left(\pi n \right)}}{\pi^{2} n^{2}} - \frac{1}{\pi^{2} n^{2}} & \text{for}\: n > -\infty \wedge n < \infty \wedge n \neq 0 \\\frac{1}{2} & \text{otherwise} \end{cases} 
Piecewise((-1/(pi^2*n^2) + sin(pi*n)/(pi*n) + cos(pi*n)/(pi^2*n^2), (n > -oo)∧(n < oo)∧(Ne(n, 0))), (1/2, True))

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

    © Sr Examen – Калькулятор