Sr Examen
Integral de absolute(sin((pi/4)*n))^2 dn
Solución
Ha introducido
[src]
pi -- 2 / | | 2 | | /pi \| | |sin|--*n|| dn | | \4 /| | / -pi ---- 2
$$\int\limits_{- \frac{\pi}{2}}^{\frac{\pi}{2}} \left|{\sin{\left(n \frac{\pi}{4} \right)}}\right|^{2}\, dn$$
Integral(Abs(sin((pi/4)*n))^2, (n, -pi/2, pi/2))
Respuesta
[src]
/ / 2\ / 2\\ / / 2\ / 2\\
| |pi | |pi || | |pi | |pi ||
| 2 cos|---|*sin|---|| | 2 cos|---|*sin|---||
| pi \ 8 / \ 8 /| |pi \ 8 / \ 8 /|
4*|- --- + -----------------| 4*|--- - -----------------|
\ 16 2 / \ 16 2 /
- ----------------------------- + ---------------------------
pi pi
$$- \frac{4 \left(- \frac{\pi^{2}}{16} + \frac{\sin{\left(\frac{\pi^{2}}{8} \right)} \cos{\left(\frac{\pi^{2}}{8} \right)}}{2}\right)}{\pi} + \frac{4 \left(- \frac{\sin{\left(\frac{\pi^{2}}{8} \right)} \cos{\left(\frac{\pi^{2}}{8} \right)}}{2} + \frac{\pi^{2}}{16}\right)}{\pi}$$
=
=
/ / 2\ / 2\\ / / 2\ / 2\\
| |pi | |pi || | |pi | |pi ||
| 2 cos|---|*sin|---|| | 2 cos|---|*sin|---||
| pi \ 8 / \ 8 /| |pi \ 8 / \ 8 /|
4*|- --- + -----------------| 4*|--- - -----------------|
\ 16 2 / \ 16 2 /
- ----------------------------- + ---------------------------
pi pi
$$- \frac{4 \left(- \frac{\pi^{2}}{16} + \frac{\sin{\left(\frac{\pi^{2}}{8} \right)} \cos{\left(\frac{\pi^{2}}{8} \right)}}{2}\right)}{\pi} + \frac{4 \left(- \frac{\sin{\left(\frac{\pi^{2}}{8} \right)} \cos{\left(\frac{\pi^{2}}{8} \right)}}{2} + \frac{\pi^{2}}{16}\right)}{\pi}$$
-4*(-pi^2/16 + cos(pi^2/8)*sin(pi^2/8)/2)/pi + 4*(pi^2/16 - cos(pi^2/8)*sin(pi^2/8)/2)/pi
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.