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