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