Sr Examen
Integral de sin(w*t)*sin(2*w*t) dt
Solución
Ha introducido
[src]
n / | | sin(w*t)*sin(2*w*t) dt | / 0
$$\int\limits_{0}^{n} \sin{\left(t w \right)} \sin{\left(t 2 w \right)}\, dt$$
Integral(sin(w*t)*sin((2*w)*t), (t, 0, n))
Respuesta (Indefinida)
[src]
/sin(t*w) /sin(3*t*w)
|-------- for w != 0 |---------- for 3*w != 0
< w < 3*w
/ | |
| \ t otherwise \ t otherwise
| sin(w*t)*sin(2*w*t) dt = C + --------------------- - -------------------------
| 2 2
/
$$\int \sin{\left(t w \right)} \sin{\left(t 2 w \right)}\, dt = C + \frac{\begin{cases} \frac{\sin{\left(t w \right)}}{w} & \text{for}\: w \neq 0 \\t & \text{otherwise} \end{cases}}{2} - \frac{\begin{cases} \frac{\sin{\left(3 t w \right)}}{3 w} & \text{for}\: 3 w \neq 0 \\t & \text{otherwise} \end{cases}}{2}$$
Respuesta
[src]
/ 2*cos(2*n*w)*sin(n*w) cos(n*w)*sin(2*n*w) |- --------------------- + ------------------- for And(w > -oo, w < oo, w != 0) < 3*w 3*w | \ 0 otherwise
$$\begin{cases} - \frac{2 \sin{\left(n w \right)} \cos{\left(2 n w \right)}}{3 w} + \frac{\sin{\left(2 n w \right)} \cos{\left(n w \right)}}{3 w} & \text{for}\: w > -\infty \wedge w < \infty \wedge w \neq 0 \\0 & \text{otherwise} \end{cases}$$
=
=
/ 2*cos(2*n*w)*sin(n*w) cos(n*w)*sin(2*n*w) |- --------------------- + ------------------- for And(w > -oo, w < oo, w != 0) < 3*w 3*w | \ 0 otherwise
$$\begin{cases} - \frac{2 \sin{\left(n w \right)} \cos{\left(2 n w \right)}}{3 w} + \frac{\sin{\left(2 n w \right)} \cos{\left(n w \right)}}{3 w} & \text{for}\: w > -\infty \wedge w < \infty \wedge w \neq 0 \\0 & \text{otherwise} \end{cases}$$
Piecewise((-2*cos(2*n*w)*sin(n*w)/(3*w) + cos(n*w)*sin(2*n*w)/(3*w), (w > -oo)∧(w < oo)∧(Ne(w, 0))), (0, True))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.