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