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