Sr Examen
Integral de (√2/π)*(sin(x/2)(cos(n*x)))dx dx
Solución
Ha introducido
[src]
2*pi / | | ___ | \/ 2 /x\ | -----*sin|-|*cos(n*x) dx | pi \2/ | / 0
$$\int\limits_{0}^{2 \pi} \frac{\sqrt{2}}{\pi} \sin{\left(\frac{x}{2} \right)} \cos{\left(n x \right)}\, dx$$
Integral((sqrt(2)/pi)*(sin(x/2)*cos(n*x)), (x, 0, 2*pi))
Respuesta
[src]
/ 0 for Or(n = -1/2, n = 1/2) | | ___ ___ < 2*\/ 2 2*\/ 2 *cos(2*pi*n) |- -------------- - ------------------- otherwise | / 2\ / 2\ \ pi*\-1 + 4*n / pi*\-1 + 4*n /
$$\begin{cases} 0 & \text{for}\: n = - \frac{1}{2} \vee n = \frac{1}{2} \\- \frac{2 \sqrt{2} \cos{\left(2 \pi n \right)}}{\pi \left(4 n^{2} - 1\right)} - \frac{2 \sqrt{2}}{\pi \left(4 n^{2} - 1\right)} & \text{otherwise} \end{cases}$$
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/ 0 for Or(n = -1/2, n = 1/2) | | ___ ___ < 2*\/ 2 2*\/ 2 *cos(2*pi*n) |- -------------- - ------------------- otherwise | / 2\ / 2\ \ pi*\-1 + 4*n / pi*\-1 + 4*n /
$$\begin{cases} 0 & \text{for}\: n = - \frac{1}{2} \vee n = \frac{1}{2} \\- \frac{2 \sqrt{2} \cos{\left(2 \pi n \right)}}{\pi \left(4 n^{2} - 1\right)} - \frac{2 \sqrt{2}}{\pi \left(4 n^{2} - 1\right)} & \text{otherwise} \end{cases}$$
Piecewise((0, (n = -1/2)∨(n = 1/2)), (-2*sqrt(2)/(pi*(-1 + 4*n^2)) - 2*sqrt(2)*cos(2*pi*n)/(pi*(-1 + 4*n^2)), True))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.