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