Sr Examen
Integral de 245*pi*sin(4*pi*x)*sin(pi*n*x/4) dx
Solución
Ha introducido
[src]
4 / | | /pi*n*x\ | 245*pi*sin(4*pi*x)*sin|------| dx | \ 4 / | / 0
$$\int\limits_{0}^{4} 245 \pi \sin{\left(4 \pi x \right)} \sin{\left(\frac{x \pi n}{4} \right)}\, dx$$
Integral(((245*pi)*sin((4*pi)*x))*sin(((pi*n)*x)/4), (x, 0, 4))
Respuesta (Indefinida)
[src]
// / pi*n*x\ / / pi*n*x\ \
|| 8*tan|-2*pi*x + ------| | 8*tan|2*pi*x + ------| |
|| \ 8 / | \ 8 / |
||-------------------------------------------------------------------------- for n != 16 |----------------------------------------------------------------------- for n != -16|
|< 2/ pi*n*x\ 2/ pi*n*x\ < 2/ pi*n*x\ 2/ pi*n*x\ |
||-16*pi + pi*n - 16*pi*tan |-2*pi*x + ------| + pi*n*tan |-2*pi*x + ------| |16*pi + pi*n + 16*pi*tan |2*pi*x + ------| + pi*n*tan |2*pi*x + ------| |
/ || \ 8 / \ 8 / | \ 8 / \ 8 / |
| || | |
| /pi*n*x\ |\ x otherwise \ x otherwise |
| 245*pi*sin(4*pi*x)*sin|------| dx = C + 245*pi*|---------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------|
| \ 4 / \ 2 2 /
|
/
$$\int 245 \pi \sin{\left(4 \pi x \right)} \sin{\left(\frac{x \pi n}{4} \right)}\, dx = C + 245 \pi \left(\frac{\begin{cases} \frac{8 \tan{\left(\frac{\pi n x}{8} - 2 \pi x \right)}}{\pi n \tan^{2}{\left(\frac{\pi n x}{8} - 2 \pi x \right)} + \pi n - 16 \pi \tan^{2}{\left(\frac{\pi n x}{8} - 2 \pi x \right)} - 16 \pi} & \text{for}\: n \neq 16 \\x & \text{otherwise} \end{cases}}{2} - \frac{\begin{cases} \frac{8 \tan{\left(\frac{\pi n x}{8} + 2 \pi x \right)}}{\pi n \tan^{2}{\left(\frac{\pi n x}{8} + 2 \pi x \right)} + \pi n + 16 \pi \tan^{2}{\left(\frac{\pi n x}{8} + 2 \pi x \right)} + 16 \pi} & \text{for}\: n \neq -16 \\x & \text{otherwise} \end{cases}}{2}\right)$$
Respuesta
[src]
/ -490*pi for n = -16 | | 490*pi for n = 16 | <15680*pi*sin(pi*n) |------------------ otherwise | 2 | -256*pi + pi*n \
$$\begin{cases} - 490 \pi & \text{for}\: n = -16 \\490 \pi & \text{for}\: n = 16 \\\frac{15680 \pi \sin{\left(\pi n \right)}}{\pi n^{2} - 256 \pi} & \text{otherwise} \end{cases}$$
=
=
/ -490*pi for n = -16 | | 490*pi for n = 16 | <15680*pi*sin(pi*n) |------------------ otherwise | 2 | -256*pi + pi*n \
$$\begin{cases} - 490 \pi & \text{for}\: n = -16 \\490 \pi & \text{for}\: n = 16 \\\frac{15680 \pi \sin{\left(\pi n \right)}}{\pi n^{2} - 256 \pi} & \text{otherwise} \end{cases}$$
Piecewise((-490*pi, n = -16), (490*pi, n = 16), (15680*pi*sin(pi*n)/(-256*pi + pi*n^2), True))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.