Sr Examen
Integral de (-5x-2)*cos(pi*n*x/2) dx
Solución
Ha introducido
[src]
2 / | | /pi*n*x\ | (-5*x - 2)*cos|------| dx | \ 2 / | / 0
$$\int\limits_{0}^{2} \left(- 5 x - 2\right) \cos{\left(\frac{x \pi n}{2} \right)}\, dx$$
Integral((-5*x - 2)*cos(((pi*n)*x)/2), (x, 0, 2))
Respuesta (Indefinida)
[src]
// 2 \
|| x |
|| -- for n = 0|
|| 2 |
/ // x for n = 0\ || | // x for n = 0\
| || | || // /pi*n*x\ \ | || |
| /pi*n*x\ || /pi*n*x\ | || ||-2*cos|------| | | || /pi*n*x\ |
| (-5*x - 2)*cos|------| dx = C - 2*|<2*sin|------| | + 5*|< || \ 2 / pi*n | | - 5*x*|<2*sin|------| |
| \ 2 / || \ 2 / | ||2*|<-------------- for ---- != 0| | || \ 2 / |
| ||------------- otherwise| || || pi*n 2 | | ||------------- otherwise|
/ \\ pi*n / || || | | \\ pi*n /
|| \\ 0 otherwise / |
||---------------------------------- otherwise|
|| pi*n |
\\ /
$$\int \left(- 5 x - 2\right) \cos{\left(\frac{x \pi n}{2} \right)}\, dx = C - 5 x \left(\begin{cases} x & \text{for}\: n = 0 \\\frac{2 \sin{\left(\frac{\pi n x}{2} \right)}}{\pi n} & \text{otherwise} \end{cases}\right) - 2 \left(\begin{cases} x & \text{for}\: n = 0 \\\frac{2 \sin{\left(\frac{\pi n x}{2} \right)}}{\pi n} & \text{otherwise} \end{cases}\right) + 5 \left(\begin{cases} \frac{x^{2}}{2} & \text{for}\: n = 0 \\\frac{2 \left(\begin{cases} - \frac{2 \cos{\left(\frac{\pi n x}{2} \right)}}{\pi n} & \text{for}\: \frac{\pi n}{2} \neq 0 \\0 & \text{otherwise} \end{cases}\right)}{\pi n} & \text{otherwise} \end{cases}\right)$$
Respuesta
[src]
/ 20 24*sin(pi*n) 20*cos(pi*n) |------ - ------------ - ------------ for And(n > -oo, n < oo, n != 0) | 2 2 pi*n 2 2
$$\begin{cases} - \frac{24 \sin{\left(\pi n \right)}}{\pi n} - \frac{20 \cos{\left(\pi n \right)}}{\pi^{2} n^{2}} + \frac{20}{\pi^{2} n^{2}} & \text{for}\: n > -\infty \wedge n < \infty \wedge n \neq 0 \\-14 & \text{otherwise} \end{cases}$$
=
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/ 20 24*sin(pi*n) 20*cos(pi*n) |------ - ------------ - ------------ for And(n > -oo, n < oo, n != 0) | 2 2 pi*n 2 2
$$\begin{cases} - \frac{24 \sin{\left(\pi n \right)}}{\pi n} - \frac{20 \cos{\left(\pi n \right)}}{\pi^{2} n^{2}} + \frac{20}{\pi^{2} n^{2}} & \text{for}\: n > -\infty \wedge n < \infty \wedge n \neq 0 \\-14 & \text{otherwise} \end{cases}$$
Piecewise((20/(pi^2*n^2) - 24*sin(pi*n)/(pi*n) - 20*cos(pi*n)/(pi^2*n^2), (n > -oo)∧(n < oo)∧(Ne(n, 0))), (-14, True))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.