Sr Examen
Integral de cos((2n-1)*x/5) dx
Solución
Ha introducido
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1 / | | /(2*n - 1)*x\ | cos|-----------| dx | \ 5 / | / 0
$$\int\limits_{0}^{1} \cos{\left(\frac{x \left(2 n - 1\right)}{5} \right)}\, dx$$
Integral(cos(((2*n - 1)*x)/5), (x, 0, 1))
Respuesta (Indefinida)
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/ // /(2*n - 1)*x\ \ | ||5*sin|-----------| | | /(2*n - 1)*x\ || \ 5 / | | cos|-----------| dx = C + |<------------------ for -1 + 2*n != 0| | \ 5 / || -1 + 2*n | | || | / \\ x otherwise /
$$\int \cos{\left(\frac{x \left(2 n - 1\right)}{5} \right)}\, dx = C + \begin{cases} \frac{5 \sin{\left(\frac{x \left(2 n - 1\right)}{5} \right)}}{2 n - 1} & \text{for}\: 2 n - 1 \neq 0 \\x & \text{otherwise} \end{cases}$$
Respuesta
[src]
/ / 1 2*n\ |sin|- - + ---| | \ 5 5 / |-------------- for And(n > -oo, n < oo, n != 1/2) < 1 2*n | - - + --- | 5 5 | \ 1 otherwise
$$\begin{cases} \frac{\sin{\left(\frac{2 n}{5} - \frac{1}{5} \right)}}{\frac{2 n}{5} - \frac{1}{5}} & \text{for}\: n > -\infty \wedge n < \infty \wedge n \neq \frac{1}{2} \\1 & \text{otherwise} \end{cases}$$
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/ / 1 2*n\ |sin|- - + ---| | \ 5 5 / |-------------- for And(n > -oo, n < oo, n != 1/2) < 1 2*n | - - + --- | 5 5 | \ 1 otherwise
$$\begin{cases} \frac{\sin{\left(\frac{2 n}{5} - \frac{1}{5} \right)}}{\frac{2 n}{5} - \frac{1}{5}} & \text{for}\: n > -\infty \wedge n < \infty \wedge n \neq \frac{1}{2} \\1 & \text{otherwise} \end{cases}$$
Piecewise((sin(-1/5 + 2*n/5)/(-1/5 + 2*n/5), (n > -oo)∧(n < oo)∧(Ne(n, 1/2))), (1, True))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.