Sr Examen
Integral de x/7*sin(px) dx
Solución
Ha introducido
[src]
14 / | | x | -*sin(p*x) dx | 7 | / 0
$$\int\limits_{0}^{14} \frac{x}{7} \sin{\left(p x \right)}\, dx$$
Integral((x/7)*sin(p*x), (x, 0, 14))
Respuesta (Indefinida)
[src]
/ 0 for p = 0
|
| //sin(p*x) \
| ||-------- for p != 0|
<-|< p | // 0 for p = 0\
| || | || |
/ | \\ x otherwise / x*|<-cos(p*x) |
| |------------------------- otherwise ||---------- otherwise|
| x \ p \\ p /
| -*sin(p*x) dx = C - ------------------------------------- + --------------------------
| 7 7 7
|
/
$$\int \frac{x}{7} \sin{\left(p x \right)}\, dx = C + \frac{x \left(\begin{cases} 0 & \text{for}\: p = 0 \\- \frac{\cos{\left(p x \right)}}{p} & \text{otherwise} \end{cases}\right)}{7} - \frac{\begin{cases} 0 & \text{for}\: p = 0 \\- \frac{\begin{cases} \frac{\sin{\left(p x \right)}}{p} & \text{for}\: p \neq 0 \\x & \text{otherwise} \end{cases}}{p} & \text{otherwise} \end{cases}}{7}$$
Respuesta
[src]
/ 2*cos(14*p) sin(14*p) |- ----------- + --------- for And(p > -oo, p < oo, p != 0) | p 2 < 7*p | | 0 otherwise \
$$\begin{cases} - \frac{2 \cos{\left(14 p \right)}}{p} + \frac{\sin{\left(14 p \right)}}{7 p^{2}} & \text{for}\: p > -\infty \wedge p < \infty \wedge p \neq 0 \\0 & \text{otherwise} \end{cases}$$
=
=
/ 2*cos(14*p) sin(14*p) |- ----------- + --------- for And(p > -oo, p < oo, p != 0) | p 2 < 7*p | | 0 otherwise \
$$\begin{cases} - \frac{2 \cos{\left(14 p \right)}}{p} + \frac{\sin{\left(14 p \right)}}{7 p^{2}} & \text{for}\: p > -\infty \wedge p < \infty \wedge p \neq 0 \\0 & \text{otherwise} \end{cases}$$
Piecewise((-2*cos(14*p)/p + sin(14*p)/(7*p^2), (p > -oo)∧(p < oo)∧(Ne(p, 0))), (0, True))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.