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