Sr Examen
Integral de cos(t)*cos(w*t)*dt dx
Solución
Ha introducido
[src]
pi -- 2 / | | cos(t)*cos(w*t) dt | / 0
$$\int\limits_{0}^{\frac{\pi}{2}} \cos{\left(t \right)} \cos{\left(t w \right)}\, dt$$
Integral(cos(t)*cos(w*t), (t, 0, pi/2))
Respuesta (Indefinida)
[src]
/ /t t*w\ / / t t*w\
| 2*tan|- + ---| | 2*tan|- - + ---|
| \2 2 / | \ 2 2 /
|--------------------------------------- for w != -1 |-------------------------------------------- for w != 1
< 2/t t*w\ 2/t t*w\ < 2/ t t*w\ 2/ t t*w\
|1 + w + tan |- + ---| + w*tan |- + ---| |-1 + w - tan |- - + ---| + w*tan |- - + ---|
| \2 2 / \2 2 / | \ 2 2 / \ 2 2 /
/ | |
| \ t otherwise \ t otherwise
| cos(t)*cos(w*t) dt = C + ----------------------------------------------------- + ---------------------------------------------------------
| 2 2
/
$$\int \cos{\left(t \right)} \cos{\left(t w \right)}\, dt = C + \frac{\begin{cases} \frac{2 \tan{\left(\frac{t w}{2} - \frac{t}{2} \right)}}{w \tan^{2}{\left(\frac{t w}{2} - \frac{t}{2} \right)} + w - \tan^{2}{\left(\frac{t w}{2} - \frac{t}{2} \right)} - 1} & \text{for}\: w \neq 1 \\t & \text{otherwise} \end{cases}}{2} + \frac{\begin{cases} \frac{2 \tan{\left(\frac{t w}{2} + \frac{t}{2} \right)}}{w \tan^{2}{\left(\frac{t w}{2} + \frac{t}{2} \right)} + w + \tan^{2}{\left(\frac{t w}{2} + \frac{t}{2} \right)} + 1} & \text{for}\: w \neq -1 \\t & \text{otherwise} \end{cases}}{2}$$
Respuesta
[src]
/ pi | -- for Or(w = -1, w = 1) | 4 | | /pi*w\ <-cos|----| | \ 2 / |----------- otherwise | 2 | -1 + w \
$$\begin{cases} \frac{\pi}{4} & \text{for}\: w = -1 \vee w = 1 \\- \frac{\cos{\left(\frac{\pi w}{2} \right)}}{w^{2} - 1} & \text{otherwise} \end{cases}$$
=
=
/ pi | -- for Or(w = -1, w = 1) | 4 | | /pi*w\ <-cos|----| | \ 2 / |----------- otherwise | 2 | -1 + w \
$$\begin{cases} \frac{\pi}{4} & \text{for}\: w = -1 \vee w = 1 \\- \frac{\cos{\left(\frac{\pi w}{2} \right)}}{w^{2} - 1} & \text{otherwise} \end{cases}$$
Piecewise((pi/4, (w = -1)∨(w = 1)), (-cos(pi*w/2)/(-1 + w^2), True))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.