Sr Examen
Integral de (cos(pi*x/4))*sin(pi*n*x/3) dx
Solución
Ha introducido
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2 / | | /pi*x\ /pi*n*x\ | cos|----|*sin|------| dx | \ 4 / \ 3 / | / 0
$$\int\limits_{0}^{2} \sin{\left(\frac{x \pi n}{3} \right)} \cos{\left(\frac{\pi x}{4} \right)}\, dx$$
Integral(cos((pi*x)/4)*sin(((pi*n)*x)/3), (x, 0, 2))
Respuesta
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/ -2 | --- for n = -3/4 | pi | | 2 | -- for n = 3/4 | pi < | /2*pi*n\ | 36*sin|------| | \ 3 / 48*n |- ---------------- + ---------------- otherwise | 2 2 | -9*pi + 16*pi*n -9*pi + 16*pi*n \
$$\begin{cases} - \frac{2}{\pi} & \text{for}\: n = - \frac{3}{4} \\\frac{2}{\pi} & \text{for}\: n = \frac{3}{4} \\\frac{48 n}{16 \pi n^{2} - 9 \pi} - \frac{36 \sin{\left(\frac{2 \pi n}{3} \right)}}{16 \pi n^{2} - 9 \pi} & \text{otherwise} \end{cases}$$
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/ -2 | --- for n = -3/4 | pi | | 2 | -- for n = 3/4 | pi < | /2*pi*n\ | 36*sin|------| | \ 3 / 48*n |- ---------------- + ---------------- otherwise | 2 2 | -9*pi + 16*pi*n -9*pi + 16*pi*n \
$$\begin{cases} - \frac{2}{\pi} & \text{for}\: n = - \frac{3}{4} \\\frac{2}{\pi} & \text{for}\: n = \frac{3}{4} \\\frac{48 n}{16 \pi n^{2} - 9 \pi} - \frac{36 \sin{\left(\frac{2 \pi n}{3} \right)}}{16 \pi n^{2} - 9 \pi} & \text{otherwise} \end{cases}$$
Piecewise((-2/pi, n = -3/4), (2/pi, n = 3/4), (-36*sin(2*pi*n/3)/(-9*pi + 16*pi*n^2) + 48*n/(-9*pi + 16*pi*n^2), True))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.