Sr Examen
Integral de x^2*sin(pi*n*x/10)/4 dx
Solución
Ha introducido
[src]
10 / | | 2 /pi*n*x\ | x *sin|------| | \ 10 / | -------------- dx | 4 | / 0
$$\int\limits_{0}^{10} \frac{x^{2} \sin{\left(\frac{x \pi n}{10} \right)}}{4}\, dx$$
Integral((x^2*sin(((pi*n)*x)/10))/4, (x, 0, 10))
Respuesta (Indefinida)
[src]
/ 0 for n = 0
|
| // /pi*n*x\ /pi*n*x\ \
| ||100*cos|------| 10*x*sin|------| |
| || \ 10 / \ 10 / |
| ||--------------- + ---------------- for n != 0|
| || 2 2 pi*n |
<-10*|< pi *n |
| || | // 0 for n = 0\
| || 2 | || |
/ | || x | 2 || /pi*n*x\ |
| | || -- otherwise | x *|<-10*cos|------| |
| 2 /pi*n*x\ | \\ 2 / || \ 10 / |
| x *sin|------| |----------------------------------------------------- otherwise ||--------------- otherwise|
| \ 10 / \ pi*n \\ pi*n /
| -------------- dx = C - ----------------------------------------------------------------- + --------------------------------
| 4 2 4
|
/
$$\int \frac{x^{2} \sin{\left(\frac{x \pi n}{10} \right)}}{4}\, dx = C + \frac{x^{2} \left(\begin{cases} 0 & \text{for}\: n = 0 \\- \frac{10 \cos{\left(\frac{\pi n x}{10} \right)}}{\pi n} & \text{otherwise} \end{cases}\right)}{4} - \frac{\begin{cases} 0 & \text{for}\: n = 0 \\- \frac{10 \left(\begin{cases} \frac{10 x \sin{\left(\frac{\pi n x}{10} \right)}}{\pi n} + \frac{100 \cos{\left(\frac{\pi n x}{10} \right)}}{\pi^{2} n^{2}} & \text{for}\: n \neq 0 \\\frac{x^{2}}{2} & \text{otherwise} \end{cases}\right)}{\pi n} & \text{otherwise} \end{cases}}{2}$$
Respuesta
[src]
/ 500 250*cos(pi*n) 500*cos(pi*n) 500*sin(pi*n) |- ------ - ------------- + ------------- + ------------- for And(n > -oo, n < oo, n != 0) | 3 3 pi*n 3 3 2 2 < pi *n pi *n pi *n | | 0 otherwise \
$$\begin{cases} - \frac{250 \cos{\left(\pi n \right)}}{\pi n} + \frac{500 \sin{\left(\pi n \right)}}{\pi^{2} n^{2}} + \frac{500 \cos{\left(\pi n \right)}}{\pi^{3} n^{3}} - \frac{500}{\pi^{3} n^{3}} & \text{for}\: n > -\infty \wedge n < \infty \wedge n \neq 0 \\0 & \text{otherwise} \end{cases}$$
=
=
/ 500 250*cos(pi*n) 500*cos(pi*n) 500*sin(pi*n) |- ------ - ------------- + ------------- + ------------- for And(n > -oo, n < oo, n != 0) | 3 3 pi*n 3 3 2 2 < pi *n pi *n pi *n | | 0 otherwise \
$$\begin{cases} - \frac{250 \cos{\left(\pi n \right)}}{\pi n} + \frac{500 \sin{\left(\pi n \right)}}{\pi^{2} n^{2}} + \frac{500 \cos{\left(\pi n \right)}}{\pi^{3} n^{3}} - \frac{500}{\pi^{3} n^{3}} & \text{for}\: n > -\infty \wedge n < \infty \wedge n \neq 0 \\0 & \text{otherwise} \end{cases}$$
Piecewise((-500/(pi^3*n^3) - 250*cos(pi*n)/(pi*n) + 500*cos(pi*n)/(pi^3*n^3) + 500*sin(pi*n)/(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.