Sr Examen
Integral de sin3x*cos((pi*n*x)/4) dx
Solución
Ha introducido
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1 / | | /pi*n*x\ | sin(3*x)*cos|------| dx | \ 4 / | / 0
$$\int\limits_{0}^{1} \sin{\left(3 x \right)} \cos{\left(\frac{x \pi n}{4} \right)}\, dx$$
Integral(sin(3*x)*cos(((pi*n)*x)/4), (x, 0, 1))
Respuesta
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/ 2 | 1 cos (3) / -12 12\ | - - ------- for Or|n = ----, n = --| | 6 6 \ pi pi/ | < /pi*n\ /pi*n\ | 48*cos(3)*cos|----| 4*pi*n*sin(3)*sin|----| | 48 \ 4 / \ 4 / |- ------------- + ------------------- + ----------------------- otherwise | 2 2 2 2 2 2 \ -144 + pi *n -144 + pi *n -144 + pi *n
$$\begin{cases} \frac{1}{6} - \frac{\cos^{2}{\left(3 \right)}}{6} & \text{for}\: n = - \frac{12}{\pi} \vee n = \frac{12}{\pi} \\\frac{4 \pi n \sin{\left(3 \right)} \sin{\left(\frac{\pi n}{4} \right)}}{\pi^{2} n^{2} - 144} + \frac{48 \cos{\left(3 \right)} \cos{\left(\frac{\pi n}{4} \right)}}{\pi^{2} n^{2} - 144} - \frac{48}{\pi^{2} n^{2} - 144} & \text{otherwise} \end{cases}$$
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/ 2 | 1 cos (3) / -12 12\ | - - ------- for Or|n = ----, n = --| | 6 6 \ pi pi/ | < /pi*n\ /pi*n\ | 48*cos(3)*cos|----| 4*pi*n*sin(3)*sin|----| | 48 \ 4 / \ 4 / |- ------------- + ------------------- + ----------------------- otherwise | 2 2 2 2 2 2 \ -144 + pi *n -144 + pi *n -144 + pi *n
$$\begin{cases} \frac{1}{6} - \frac{\cos^{2}{\left(3 \right)}}{6} & \text{for}\: n = - \frac{12}{\pi} \vee n = \frac{12}{\pi} \\\frac{4 \pi n \sin{\left(3 \right)} \sin{\left(\frac{\pi n}{4} \right)}}{\pi^{2} n^{2} - 144} + \frac{48 \cos{\left(3 \right)} \cos{\left(\frac{\pi n}{4} \right)}}{\pi^{2} n^{2} - 144} - \frac{48}{\pi^{2} n^{2} - 144} & \text{otherwise} \end{cases}$$
Piecewise((1/6 - cos(3)^2/6, (n = -12/pi)∨(n = 12/pi)), (-48/(-144 + pi^2*n^2) + 48*cos(3)*cos(pi*n/4)/(-144 + pi^2*n^2) + 4*pi*n*sin(3)*sin(pi*n/4)/(-144 + pi^2*n^2), True))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.