Sr Examen
Integral de xsin(kx) dx
Solución
Ha introducido
[src]
1 / | | x*sin(k*x) dx | / 0
$$\int\limits_{0}^{1} x \sin{\left(k x \right)}\, dx$$
Integral(x*sin(k*x), (x, 0, 1))
Respuesta (Indefinida)
[src]
// 0 for k = 0\
|| |
/ || //sin(k*x) \ | // 0 for k = 0\
| || ||-------- for k != 0| | || |
| x*sin(k*x) dx = C - |<-|< k | | + x*|<-cos(k*x) |
| || || | | ||---------- otherwise|
/ || \\ x otherwise / | \\ k /
||------------------------- otherwise|
\\ k /
$$\int x \sin{\left(k x \right)}\, dx = C + x \left(\begin{cases} 0 & \text{for}\: k = 0 \\- \frac{\cos{\left(k x \right)}}{k} & \text{otherwise} \end{cases}\right) - \begin{cases} 0 & \text{for}\: k = 0 \\- \frac{\begin{cases} \frac{\sin{\left(k x \right)}}{k} & \text{for}\: k \neq 0 \\x & \text{otherwise} \end{cases}}{k} & \text{otherwise} \end{cases}$$
Respuesta
[src]
/sin(k) cos(k) |------ - ------ for And(k > -oo, k < oo, k != 0) | 2 k < k | | 0 otherwise \
$$\begin{cases} - \frac{\cos{\left(k \right)}}{k} + \frac{\sin{\left(k \right)}}{k^{2}} & \text{for}\: k > -\infty \wedge k < \infty \wedge k \neq 0 \\0 & \text{otherwise} \end{cases}$$
=
=
/sin(k) cos(k) |------ - ------ for And(k > -oo, k < oo, k != 0) | 2 k < k | | 0 otherwise \
$$\begin{cases} - \frac{\cos{\left(k \right)}}{k} + \frac{\sin{\left(k \right)}}{k^{2}} & \text{for}\: k > -\infty \wedge k < \infty \wedge k \neq 0 \\0 & \text{otherwise} \end{cases}$$
Piecewise((sin(k)/k^2 - cos(k)/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.