Sr Examen
Integral de (sin(4pix))*sin((pi*n*x)/2) dx
Solución
Ha introducido
[src]
2 / | | /pi*n*x\ | sin(4*pi*x)*sin|------| dx | \ 2 / | / 0
$$\int\limits_{0}^{2} \sin{\left(\frac{x \pi n}{2} \right)} \sin{\left(4 \pi x \right)}\, dx$$
Integral(sin((4*pi)*x)*sin(((pi*n)*x)/2), (x, 0, 2))
Respuesta (Indefinida)
[src]
/ / pi*n*x\ / / pi*n*x\
| 4*tan|-2*pi*x + ------| | 4*tan|2*pi*x + ------|
| \ 4 / | \ 4 /
|------------------------------------------------------------------------ for n != 8 |--------------------------------------------------------------------- for n != -8
< 2/ pi*n*x\ 2/ pi*n*x\ < 2/ pi*n*x\ 2/ pi*n*x\
|-8*pi + pi*n - 8*pi*tan |-2*pi*x + ------| + pi*n*tan |-2*pi*x + ------| |8*pi + pi*n + 8*pi*tan |2*pi*x + ------| + pi*n*tan |2*pi*x + ------|
/ | \ 4 / \ 4 / | \ 4 / \ 4 /
| | |
| /pi*n*x\ \ x otherwise \ x otherwise
| sin(4*pi*x)*sin|------| dx = C + ------------------------------------------------------------------------------------- - -----------------------------------------------------------------------------------
| \ 2 / 2 2
|
/
$$\int \sin{\left(\frac{x \pi n}{2} \right)} \sin{\left(4 \pi x \right)}\, dx = C + \frac{\begin{cases} \frac{4 \tan{\left(\frac{\pi n x}{4} - 2 \pi x \right)}}{\pi n \tan^{2}{\left(\frac{\pi n x}{4} - 2 \pi x \right)} + \pi n - 8 \pi \tan^{2}{\left(\frac{\pi n x}{4} - 2 \pi x \right)} - 8 \pi} & \text{for}\: n \neq 8 \\x & \text{otherwise} \end{cases}}{2} - \frac{\begin{cases} \frac{4 \tan{\left(\frac{\pi n x}{4} + 2 \pi x \right)}}{\pi n \tan^{2}{\left(\frac{\pi n x}{4} + 2 \pi x \right)} + \pi n + 8 \pi \tan^{2}{\left(\frac{\pi n x}{4} + 2 \pi x \right)} + 8 \pi} & \text{for}\: n \neq -8 \\x & \text{otherwise} \end{cases}}{2}$$
Respuesta
[src]
/ -1 for n = -8 | | 1 for n = 8 | < 16*sin(pi*n) |-------------- otherwise | 2 |-64*pi + pi*n \
$$\begin{cases} -1 & \text{for}\: n = -8 \\1 & \text{for}\: n = 8 \\\frac{16 \sin{\left(\pi n \right)}}{\pi n^{2} - 64 \pi} & \text{otherwise} \end{cases}$$
=
=
/ -1 for n = -8 | | 1 for n = 8 | < 16*sin(pi*n) |-------------- otherwise | 2 |-64*pi + pi*n \
$$\begin{cases} -1 & \text{for}\: n = -8 \\1 & \text{for}\: n = 8 \\\frac{16 \sin{\left(\pi n \right)}}{\pi n^{2} - 64 \pi} & \text{otherwise} \end{cases}$$
Piecewise((-1, n = -8), (1, n = 8), (16*sin(pi*n)/(-64*pi + pi*n^2), True))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.