Sr Examen
Integral de (6-x)*cos(n*x*pi/4) dx
Solución
Ha introducido
[src]
4 / | | /n*x*pi\ | (6 - x)*cos|------| dx | \ 4 / | / 3
$$\int\limits_{3}^{4} \left(6 - x\right) \cos{\left(\frac{\pi n x}{4} \right)}\, dx$$
Integral((6 - x)*cos(((n*x)*pi)/4), (x, 3, 4))
Respuesta (Indefinida)
[src]
// 2 \
|| x |
|| -- for n = 0|
|| 2 |
/ // x for n = 0\ // x for n = 0\ || |
| || | || | || // /pi*n*x\ \ |
| /n*x*pi\ || /pi*n*x\ | || /pi*n*x\ | || ||-4*cos|------| | |
| (6 - x)*cos|------| dx = C + 6*|<4*sin|------| | - x*|<4*sin|------| | + |< || \ 4 / pi*n | |
| \ 4 / || \ 4 / | || \ 4 / | ||4*|<-------------- for ---- != 0| |
| ||------------- otherwise| ||------------- otherwise| || || pi*n 4 | |
/ \\ pi*n / \\ pi*n / || || | |
|| \\ 0 otherwise / |
||---------------------------------- otherwise|
|| pi*n |
\\ /
$$\int \left(6 - x\right) \cos{\left(\frac{\pi n x}{4} \right)}\, dx = C - x \left(\begin{cases} x & \text{for}\: n = 0 \\\frac{4 \sin{\left(\frac{\pi n x}{4} \right)}}{\pi n} & \text{otherwise} \end{cases}\right) + 6 \left(\begin{cases} x & \text{for}\: n = 0 \\\frac{4 \sin{\left(\frac{\pi n x}{4} \right)}}{\pi n} & \text{otherwise} \end{cases}\right) + \begin{cases} \frac{x^{2}}{2} & \text{for}\: n = 0 \\\frac{4 \left(\begin{cases} - \frac{4 \cos{\left(\frac{\pi n x}{4} \right)}}{\pi n} & \text{for}\: \frac{\pi n}{4} \neq 0 \\0 & \text{otherwise} \end{cases}\right)}{\pi n} & \text{otherwise} \end{cases}$$
Respuesta
[src]
/ /3*pi*n\ /3*pi*n\ | 12*sin|------| 16*cos|------| | 16*cos(pi*n) \ 4 / 8*sin(pi*n) \ 4 / |- ------------ - -------------- + ----------- + -------------- for And(n > -oo, n < oo, n != 0) < 2 2 pi*n pi*n 2 2 | pi *n pi *n | | 5/2 otherwise \
$$\begin{cases} - \frac{12 \sin{\left(\frac{3 \pi n}{4} \right)}}{\pi n} + \frac{8 \sin{\left(\pi n \right)}}{\pi n} + \frac{16 \cos{\left(\frac{3 \pi n}{4} \right)}}{\pi^{2} n^{2}} - \frac{16 \cos{\left(\pi n \right)}}{\pi^{2} n^{2}} & \text{for}\: n > -\infty \wedge n < \infty \wedge n \neq 0 \\\frac{5}{2} & \text{otherwise} \end{cases}$$
=
=
/ /3*pi*n\ /3*pi*n\ | 12*sin|------| 16*cos|------| | 16*cos(pi*n) \ 4 / 8*sin(pi*n) \ 4 / |- ------------ - -------------- + ----------- + -------------- for And(n > -oo, n < oo, n != 0) < 2 2 pi*n pi*n 2 2 | pi *n pi *n | | 5/2 otherwise \
$$\begin{cases} - \frac{12 \sin{\left(\frac{3 \pi n}{4} \right)}}{\pi n} + \frac{8 \sin{\left(\pi n \right)}}{\pi n} + \frac{16 \cos{\left(\frac{3 \pi n}{4} \right)}}{\pi^{2} n^{2}} - \frac{16 \cos{\left(\pi n \right)}}{\pi^{2} n^{2}} & \text{for}\: n > -\infty \wedge n < \infty \wedge n \neq 0 \\\frac{5}{2} & \text{otherwise} \end{cases}$$
Piecewise((-16*cos(pi*n)/(pi^2*n^2) - 12*sin(3*pi*n/4)/(pi*n) + 8*sin(pi*n)/(pi*n) + 16*cos(3*pi*n/4)/(pi^2*n^2), (n > -oo)∧(n < oo)∧(Ne(n, 0))), (5/2, True))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.