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