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