Sr Examen
Integral de (2/3(x-1))cos(nx) dx
Solución
Ha introducido
[src]
4 / | | 2*(x - 1) | ---------*cos(n*x) dx | 3 | / -4
$$\int\limits_{-4}^{4} \frac{2 \left(x - 1\right)}{3} \cos{\left(n x \right)}\, dx$$
Integral((2*(x - 1)/3)*cos(n*x), (x, -4, 4))
Respuesta (Indefinida)
[src]
// 2 \
|| x |
|| -- for n = 0|
|| 2 |
|| |
||/-cos(n*x) |
2*|<|---------- for n != 0 |
||< n |
// x for n = 0\ ||| | // x for n = 0\
|| | ||\ 0 otherwise | || |
/ 2*|
$$\int \frac{2 \left(x - 1\right)}{3} \cos{\left(n x \right)}\, dx = C + \frac{2 x \left(\begin{cases} x & \text{for}\: n = 0 \\\frac{\sin{\left(n x \right)}}{n} & \text{otherwise} \end{cases}\right)}{3} - \frac{2 \left(\begin{cases} x & \text{for}\: n = 0 \\\frac{\sin{\left(n x \right)}}{n} & \text{otherwise} \end{cases}\right)}{3} - \frac{2 \left(\begin{cases} \frac{x^{2}}{2} & \text{for}\: n = 0 \\\frac{\begin{cases} - \frac{\cos{\left(n x \right)}}{n} & \text{for}\: n \neq 0 \\0 & \text{otherwise} \end{cases}}{n} & \text{otherwise} \end{cases}\right)}{3}$$
Respuesta
[src]
/-4*sin(4*n) |----------- for And(n > -oo, n < oo, n != 0) < 3*n | \ -16/3 otherwise
$$\begin{cases} - \frac{4 \sin{\left(4 n \right)}}{3 n} & \text{for}\: n > -\infty \wedge n < \infty \wedge n \neq 0 \\- \frac{16}{3} & \text{otherwise} \end{cases}$$
=
=
/-4*sin(4*n) |----------- for And(n > -oo, n < oo, n != 0) < 3*n | \ -16/3 otherwise
$$\begin{cases} - \frac{4 \sin{\left(4 n \right)}}{3 n} & \text{for}\: n > -\infty \wedge n < \infty \wedge n \neq 0 \\- \frac{16}{3} & \text{otherwise} \end{cases}$$
Piecewise((-4*sin(4*n)/(3*n), (n > -oo)∧(n < oo)∧(Ne(n, 0))), (-16/3, True))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.