Sr Examen
Integral de 2x*sin(kx) dx
Solución
Ha introducido
[src]
3*pi ---- 2 / | | 2*x*sin(k*x) dx | / 0
$$\int\limits_{0}^{\frac{3 \pi}{2}} 2 x \sin{\left(k x \right)}\, dx$$
Integral((2*x)*sin(k*x), (x, 0, 3*pi/2))
Respuesta (Indefinida)
[src]
// 0 for k = 0\
|| |
/ || //sin(k*x) \ | // 0 for k = 0\
| || ||-------- for k != 0| | || |
| 2*x*sin(k*x) dx = C - 2*|<-|< k | | + 2*x*|<-cos(k*x) |
| || || | | ||---------- otherwise|
/ || \\ x otherwise / | \\ k /
||------------------------- otherwise|
\\ k /
$$\int 2 x \sin{\left(k x \right)}\, dx = C + 2 x \left(\begin{cases} 0 & \text{for}\: k = 0 \\- \frac{\cos{\left(k x \right)}}{k} & \text{otherwise} \end{cases}\right) - 2 \left(\begin{cases} 0 & \text{for}\: k = 0 \\- \frac{\begin{cases} \frac{\sin{\left(k x \right)}}{k} & \text{for}\: k \neq 0 \\x & \text{otherwise} \end{cases}}{k} & \text{otherwise} \end{cases}\right)$$
Respuesta
[src]
/ /3*pi*k\ /3*pi*k\ |2*sin|------| 3*pi*cos|------| | \ 2 / \ 2 / |------------- - ---------------- for And(k > -oo, k < oo, k != 0) < 2 k | k | | 0 otherwise \
$$\begin{cases} - \frac{3 \pi \cos{\left(\frac{3 \pi k}{2} \right)}}{k} + \frac{2 \sin{\left(\frac{3 \pi k}{2} \right)}}{k^{2}} & \text{for}\: k > -\infty \wedge k < \infty \wedge k \neq 0 \\0 & \text{otherwise} \end{cases}$$
=
=
/ /3*pi*k\ /3*pi*k\ |2*sin|------| 3*pi*cos|------| | \ 2 / \ 2 / |------------- - ---------------- for And(k > -oo, k < oo, k != 0) < 2 k | k | | 0 otherwise \
$$\begin{cases} - \frac{3 \pi \cos{\left(\frac{3 \pi k}{2} \right)}}{k} + \frac{2 \sin{\left(\frac{3 \pi k}{2} \right)}}{k^{2}} & \text{for}\: k > -\infty \wedge k < \infty \wedge k \neq 0 \\0 & \text{otherwise} \end{cases}$$
Piecewise((2*sin(3*pi*k/2)/k^2 - 3*pi*cos(3*pi*k/2)/k, (k > -oo)∧(k < oo)∧(Ne(k, 0))), (0, True))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.