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