Sr Examen
Integral de 3*(r/b)*cos(2x)*cos(mx)+2*sin(3x)*cos(mx) dx
Solución
Ha introducido
[src]
pi / | | / r \ | |3*-*cos(2*x)*cos(m*x) + 2*sin(3*x)*cos(m*x)| dx | \ b / | / 0
$$\int\limits_{0}^{\pi} \left(3 \frac{r}{b} \cos{\left(2 x \right)} \cos{\left(m x \right)} + 2 \sin{\left(3 x \right)} \cos{\left(m x \right)}\right)\, dx$$
Integral(((3*(r/b))*cos(2*x))*cos(m*x) + (2*sin(3*x))*cos(m*x), (x, 0, pi))
Respuesta
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/ 3*m*r*sin(pi*m) | --------------- for Or(m = -3, m = 3) | / 2\ | b*\-4 + m / | | 6 6*cos(pi*m) 3*pi*r | - ------- - ----------- + ------ for Or(m = -2, m = 2) < 2 2 2*b | -9 + m -9 + m | | 6 6*cos(pi*m) 3*m*r*sin(pi*m) |- ------- - ----------- + --------------- otherwise | 2 2 / 2\ | -9 + m -9 + m b*\-4 + m / \
$$\begin{cases} \frac{3 m r \sin{\left(\pi m \right)}}{b \left(m^{2} - 4\right)} & \text{for}\: m = -3 \vee m = 3 \\- \frac{6 \cos{\left(\pi m \right)}}{m^{2} - 9} - \frac{6}{m^{2} - 9} + \frac{3 \pi r}{2 b} & \text{for}\: m = -2 \vee m = 2 \\- \frac{6 \cos{\left(\pi m \right)}}{m^{2} - 9} - \frac{6}{m^{2} - 9} + \frac{3 m r \sin{\left(\pi m \right)}}{b \left(m^{2} - 4\right)} & \text{otherwise} \end{cases}$$
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/ 3*m*r*sin(pi*m) | --------------- for Or(m = -3, m = 3) | / 2\ | b*\-4 + m / | | 6 6*cos(pi*m) 3*pi*r | - ------- - ----------- + ------ for Or(m = -2, m = 2) < 2 2 2*b | -9 + m -9 + m | | 6 6*cos(pi*m) 3*m*r*sin(pi*m) |- ------- - ----------- + --------------- otherwise | 2 2 / 2\ | -9 + m -9 + m b*\-4 + m / \
$$\begin{cases} \frac{3 m r \sin{\left(\pi m \right)}}{b \left(m^{2} - 4\right)} & \text{for}\: m = -3 \vee m = 3 \\- \frac{6 \cos{\left(\pi m \right)}}{m^{2} - 9} - \frac{6}{m^{2} - 9} + \frac{3 \pi r}{2 b} & \text{for}\: m = -2 \vee m = 2 \\- \frac{6 \cos{\left(\pi m \right)}}{m^{2} - 9} - \frac{6}{m^{2} - 9} + \frac{3 m r \sin{\left(\pi m \right)}}{b \left(m^{2} - 4\right)} & \text{otherwise} \end{cases}$$
Piecewise((3*m*r*sin(pi*m)/(b*(-4 + m^2)), (m = -3)∨(m = 3)), (-6/(-9 + m^2) - 6*cos(pi*m)/(-9 + m^2) + 3*pi*r/(2*b), (m = -2)∨(m = 2)), (-6/(-9 + m^2) - 6*cos(pi*m)/(-9 + m^2) + 3*m*r*sin(pi*m)/(b*(-4 + m^2)), True))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.