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