Sr Examen
Integral de xsinnpix/4 dx
Solución
Ha introducido
[src]
1 / | | x*sin(n*pi*x) | ------------- dx | 4 | / 0
$$\int\limits_{0}^{1} \frac{x \sin{\left(x \pi n \right)}}{4}\, dx$$
Integral((x*sin((n*pi)*x))/4, (x, 0, 1))
Respuesta (Indefinida)
[src]
/ 0 for n = 0
|
| //sin(pi*n*x) \
| ||----------- for pi*n != 0|
<-|< pi*n | // 0 for n = 0\
| || | || |
/ | \\ x otherwise / x*|<-cos(pi*n*x) |
| |------------------------------- otherwise ||------------- otherwise|
| x*sin(n*pi*x) \ pi*n \\ pi*n /
| ------------- dx = C - ------------------------------------------- + -----------------------------
| 4 4 4
|
/
$$\int \frac{x \sin{\left(x \pi n \right)}}{4}\, dx = C + \frac{x \left(\begin{cases} 0 & \text{for}\: n = 0 \\- \frac{\cos{\left(\pi n x \right)}}{\pi n} & \text{otherwise} \end{cases}\right)}{4} - \frac{\begin{cases} 0 & \text{for}\: n = 0 \\- \frac{\begin{cases} \frac{\sin{\left(\pi n x \right)}}{\pi n} & \text{for}\: \pi n \neq 0 \\x & \text{otherwise} \end{cases}}{\pi n} & \text{otherwise} \end{cases}}{4}$$
Respuesta
[src]
/ cos(pi*n) sin(pi*n) |- --------- + --------- for And(n > -oo, n < oo, n != 0) | 4*pi*n 2 2 < 4*pi *n | | 0 otherwise \
$$\begin{cases} - \frac{\cos{\left(\pi n \right)}}{4 \pi n} + \frac{\sin{\left(\pi n \right)}}{4 \pi^{2} n^{2}} & \text{for}\: n > -\infty \wedge n < \infty \wedge n \neq 0 \\0 & \text{otherwise} \end{cases}$$
=
=
/ cos(pi*n) sin(pi*n) |- --------- + --------- for And(n > -oo, n < oo, n != 0) | 4*pi*n 2 2 < 4*pi *n | | 0 otherwise \
$$\begin{cases} - \frac{\cos{\left(\pi n \right)}}{4 \pi n} + \frac{\sin{\left(\pi n \right)}}{4 \pi^{2} n^{2}} & \text{for}\: n > -\infty \wedge n < \infty \wedge n \neq 0 \\0 & \text{otherwise} \end{cases}$$
Piecewise((-cos(pi*n)/(4*pi*n) + sin(pi*n)/(4*pi^2*n^2), (n > -oo)∧(n < oo)∧(Ne(n, 0))), (0, True))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.