Sr Examen
Integral de sintx*cos2t dx
Solución
Ha introducido
[src]
1 / | | sin(t*x)*cos(2*t) dx | / 0
$$\int\limits_{0}^{1} \sin{\left(t x \right)} \cos{\left(2 t \right)}\, dx$$
Integral(sin(t*x)*cos(2*t), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ // 0 for t = 0\ | || | | sin(t*x)*cos(2*t) dx = C + |<-cos(t*x) |*cos(2*t) | ||---------- otherwise| / \\ t /
$$\int \sin{\left(t x \right)} \cos{\left(2 t \right)}\, dx = C + \left(\begin{cases} 0 & \text{for}\: t = 0 \\- \frac{\cos{\left(t x \right)}}{t} & \text{otherwise} \end{cases}\right) \cos{\left(2 t \right)}$$
Respuesta
[src]
/cos(2*t) cos(t)*cos(2*t) |-------- - --------------- for And(t > -oo, t < oo, t != 0) < t t | \ 0 otherwise
$$\begin{cases} - \frac{\cos{\left(t \right)} \cos{\left(2 t \right)}}{t} + \frac{\cos{\left(2 t \right)}}{t} & \text{for}\: t > -\infty \wedge t < \infty \wedge t \neq 0 \\0 & \text{otherwise} \end{cases}$$
=
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/cos(2*t) cos(t)*cos(2*t) |-------- - --------------- for And(t > -oo, t < oo, t != 0) < t t | \ 0 otherwise
$$\begin{cases} - \frac{\cos{\left(t \right)} \cos{\left(2 t \right)}}{t} + \frac{\cos{\left(2 t \right)}}{t} & \text{for}\: t > -\infty \wedge t < \infty \wedge t \neq 0 \\0 & \text{otherwise} \end{cases}$$
Piecewise((cos(2*t)/t - cos(t)*cos(2*t)/t, (t > -oo)∧(t < oo)∧(Ne(t, 0))), (0, True))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.