Sr Examen
Integral de (6.5(x^2-2t)-6.5x)*cos(pi*n*x) dx
Solución
Ha introducido
[src]
1 / | | / / 2 \ \ | |13*\x - 2*t/ 13*x| | |------------- - ----|*cos(pi*n*x) dx | \ 2 2 / | / 0
$$\int\limits_{0}^{1} \left(- \frac{13 x}{2} + \frac{13 \left(- 2 t + x^{2}\right)}{2}\right) \cos{\left(x \pi n \right)}\, dx$$
Integral((13*(x^2 - 2*t)/2 - 13*x/2)*cos((pi*n)*x), (x, 0, 1))
Respuesta (Indefinida)
[src]
// 2 \
|| x |
|| -- for n = 0|
|| 2 |
|| |
||/-cos(pi*n*x) |
// 3 \ 13*|<|------------- for pi*n != 0 |
|| x | ||< pi*n |
|| -- for n = 0| ||| | // x for n = 0\ // x for n = 0\
/ || 3 | ||\ 0 otherwise | || | 2 || |
| || | ||----------------------------- otherwise| 13*x*|
$$\int \left(- \frac{13 x}{2} + \frac{13 \left(- 2 t + x^{2}\right)}{2}\right) \cos{\left(x \pi n \right)}\, dx = C - 13 t \left(\begin{cases} x & \text{for}\: n = 0 \\\frac{\sin{\left(\pi n x \right)}}{\pi n} & \text{otherwise} \end{cases}\right) + \frac{13 x^{2} \left(\begin{cases} x & \text{for}\: n = 0 \\\frac{\sin{\left(\pi n x \right)}}{\pi n} & \text{otherwise} \end{cases}\right)}{2} - \frac{13 x \left(\begin{cases} x & \text{for}\: n = 0 \\\frac{\sin{\left(\pi n x \right)}}{\pi n} & \text{otherwise} \end{cases}\right)}{2} + \frac{13 \left(\begin{cases} \frac{x^{2}}{2} & \text{for}\: n = 0 \\\frac{\begin{cases} - \frac{\cos{\left(\pi n x \right)}}{\pi n} & \text{for}\: \pi n \neq 0 \\0 & \text{otherwise} \end{cases}}{\pi n} & \text{otherwise} \end{cases}\right)}{2} - 13 \left(\begin{cases} \frac{x^{3}}{3} & \text{for}\: n = 0 \\\frac{\begin{cases} - \frac{x \cos{\left(\pi n x \right)}}{\pi n} + \frac{\sin{\left(\pi n x \right)}}{\pi^{2} n^{2}} & \text{for}\: n \neq 0 \\0 & \text{otherwise} \end{cases}}{\pi n} & \text{otherwise} \end{cases}\right)$$
Respuesta
[src]
/ 13 13*sin(pi*n) 13*cos(pi*n) 13*t*sin(pi*n) |-------- - ------------ + ------------ - -------------- for And(n > -oo, n < oo, n != 0) | 2 2 3 3 2 2 pi*n |2*pi *n pi *n 2*pi *n < | 13 | - -- - 13*t otherwise | 12 \
$$\begin{cases} - \frac{13 t \sin{\left(\pi n \right)}}{\pi n} + \frac{13 \cos{\left(\pi n \right)}}{2 \pi^{2} n^{2}} + \frac{13}{2 \pi^{2} n^{2}} - \frac{13 \sin{\left(\pi n \right)}}{\pi^{3} n^{3}} & \text{for}\: n > -\infty \wedge n < \infty \wedge n \neq 0 \\- 13 t - \frac{13}{12} & \text{otherwise} \end{cases}$$
=
=
/ 13 13*sin(pi*n) 13*cos(pi*n) 13*t*sin(pi*n) |-------- - ------------ + ------------ - -------------- for And(n > -oo, n < oo, n != 0) | 2 2 3 3 2 2 pi*n |2*pi *n pi *n 2*pi *n < | 13 | - -- - 13*t otherwise | 12 \
$$\begin{cases} - \frac{13 t \sin{\left(\pi n \right)}}{\pi n} + \frac{13 \cos{\left(\pi n \right)}}{2 \pi^{2} n^{2}} + \frac{13}{2 \pi^{2} n^{2}} - \frac{13 \sin{\left(\pi n \right)}}{\pi^{3} n^{3}} & \text{for}\: n > -\infty \wedge n < \infty \wedge n \neq 0 \\- 13 t - \frac{13}{12} & \text{otherwise} \end{cases}$$
Piecewise((13/(2*pi^2*n^2) - 13*sin(pi*n)/(pi^3*n^3) + 13*cos(pi*n)/(2*pi^2*n^2) - 13*t*sin(pi*n)/(pi*n), (n > -oo)∧(n < oo)∧(Ne(n, 0))), (-13/12 - 13*t, True))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.