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