Sr Examen
Integral de 2/3*(3x-2)sin(p*n*x/3) dx
Solución
Ha introducido
[src]
3 / | | 2*(3*x - 2) /p*n*x\ | -----------*sin|-----| dx | 3 \ 3 / | / 0
$$\int\limits_{0}^{3} \frac{2 \left(3 x - 2\right)}{3} \sin{\left(\frac{x n p}{3} \right)}\, dx$$
Integral((2*(3*x - 2)/3)*sin(((p*n)*x)/3), (x, 0, 3))
Respuesta (Indefinida)
[src]
// 0 for Or(n = 0, p = 0)\
|| |
// 0 for Or(And(n = 0, p = 0), n = 0, p = 0)\ || /n*p*x\ |
|| | 4*|<-3*cos|-----| |
/ || // /n*p*x\ \ | || \ 3 / | // 0 for Or(n = 0, p = 0)\
| || ||3*sin|-----| | | ||------------- otherwise | || |
| 2*(3*x - 2) /p*n*x\ || || \ 3 / n*p | | \\ n*p / || /n*p*x\ |
| -----------*sin|-----| dx = C - 2*|<-3*|<------------ for --- != 0| | - ---------------------------------------- + 2*x*|<-3*cos|-----| |
| 3 \ 3 / || || n*p 3 | | 3 || \ 3 / |
| || || | | ||------------- otherwise |
/ || \\ x otherwise / | \\ n*p /
||-------------------------------- otherwise |
\\ n*p /
$$\int \frac{2 \left(3 x - 2\right)}{3} \sin{\left(\frac{x n p}{3} \right)}\, dx = C + 2 x \left(\begin{cases} 0 & \text{for}\: n = 0 \vee p = 0 \\- \frac{3 \cos{\left(\frac{n p x}{3} \right)}}{n p} & \text{otherwise} \end{cases}\right) - \frac{4 \left(\begin{cases} 0 & \text{for}\: n = 0 \vee p = 0 \\- \frac{3 \cos{\left(\frac{n p x}{3} \right)}}{n p} & \text{otherwise} \end{cases}\right)}{3} - 2 \left(\begin{cases} 0 & \text{for}\: \left(n = 0 \wedge p = 0\right) \vee n = 0 \vee p = 0 \\- \frac{3 \left(\begin{cases} \frac{3 \sin{\left(\frac{n p x}{3} \right)}}{n p} & \text{for}\: \frac{n p}{3} \neq 0 \\x & \text{otherwise} \end{cases}\right)}{n p} & \text{otherwise} \end{cases}\right)$$
Respuesta
[src]
/ 0 for Or(And(n = 0, p = 0), n = 0, p = 0) | | 4 14*cos(n*p) 18*sin(n*p) <- --- - ----------- + ----------- otherwise | n*p n*p 2 2 | n *p \
$$\begin{cases} 0 & \text{for}\: \left(n = 0 \wedge p = 0\right) \vee n = 0 \vee p = 0 \\- \frac{14 \cos{\left(n p \right)}}{n p} - \frac{4}{n p} + \frac{18 \sin{\left(n p \right)}}{n^{2} p^{2}} & \text{otherwise} \end{cases}$$
=
=
/ 0 for Or(And(n = 0, p = 0), n = 0, p = 0) | | 4 14*cos(n*p) 18*sin(n*p) <- --- - ----------- + ----------- otherwise | n*p n*p 2 2 | n *p \
$$\begin{cases} 0 & \text{for}\: \left(n = 0 \wedge p = 0\right) \vee n = 0 \vee p = 0 \\- \frac{14 \cos{\left(n p \right)}}{n p} - \frac{4}{n p} + \frac{18 \sin{\left(n p \right)}}{n^{2} p^{2}} & \text{otherwise} \end{cases}$$
Piecewise((0, (n = 0)∨(p = 0)∨((n = 0)∧(p = 0))), (-4/(n*p) - 14*cos(n*p)/(n*p) + 18*sin(n*p)/(n^2*p^2), True))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.