Sr Examen
Integral de (x+9/pi)*cos(w*x)*dx dx
Solución
Ha introducido
[src]
pi / | | / 9 \ | |x + --|*cos(w*x) dx | \ pi/ | / 0
$$\int\limits_{0}^{\pi} \left(x + \frac{9}{\pi}\right) \cos{\left(w x \right)}\, dx$$
Integral((x + 9/pi)*cos(w*x), (x, 0, pi))
Respuesta (Indefinida)
[src]
/ // 2 \ \
| || x | |
| || -- for w = 0| |
| || 2 | |
// x for w = 0\ | || | // x for w = 0\|
|| | | ||/-cos(w*x) | || ||
9*|
$$\int \left(x + \frac{9}{\pi}\right) \cos{\left(w x \right)}\, dx = C + \frac{\pi \left(x \left(\begin{cases} x & \text{for}\: w = 0 \\\frac{\sin{\left(w x \right)}}{w} & \text{otherwise} \end{cases}\right) - \begin{cases} \frac{x^{2}}{2} & \text{for}\: w = 0 \\\frac{\begin{cases} - \frac{\cos{\left(w x \right)}}{w} & \text{for}\: w \neq 0 \\0 & \text{otherwise} \end{cases}}{w} & \text{otherwise} \end{cases}\right) + 9 \left(\begin{cases} x & \text{for}\: w = 0 \\\frac{\sin{\left(w x \right)}}{w} & \text{otherwise} \end{cases}\right)}{\pi}$$
Respuesta
[src]
/ 1 cos(pi*w) pi*sin(pi*w) 9*sin(pi*w) |- -- + --------- + ------------ + ----------- for And(w > -oo, w < oo, w != 0) | 2 2 w pi*w | w w < | 2 | pi | 9 + --- otherwise \ 2
$$\begin{cases} \frac{9 \sin{\left(\pi w \right)}}{\pi w} + \frac{\pi \sin{\left(\pi w \right)}}{w} + \frac{\cos{\left(\pi w \right)}}{w^{2}} - \frac{1}{w^{2}} & \text{for}\: w > -\infty \wedge w < \infty \wedge w \neq 0 \\\frac{\pi^{2}}{2} + 9 & \text{otherwise} \end{cases}$$
=
=
/ 1 cos(pi*w) pi*sin(pi*w) 9*sin(pi*w) |- -- + --------- + ------------ + ----------- for And(w > -oo, w < oo, w != 0) | 2 2 w pi*w | w w < | 2 | pi | 9 + --- otherwise \ 2
$$\begin{cases} \frac{9 \sin{\left(\pi w \right)}}{\pi w} + \frac{\pi \sin{\left(\pi w \right)}}{w} + \frac{\cos{\left(\pi w \right)}}{w^{2}} - \frac{1}{w^{2}} & \text{for}\: w > -\infty \wedge w < \infty \wedge w \neq 0 \\\frac{\pi^{2}}{2} + 9 & \text{otherwise} \end{cases}$$
Piecewise((-1/w^2 + cos(pi*w)/w^2 + pi*sin(pi*w)/w + 9*sin(pi*w)/(pi*w), (w > -oo)∧(w < oo)∧(Ne(w, 0))), (9 + pi^2/2, True))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.