Sr Examen
Integral de (1-(|x|/3))sinAt dt
Solución
Ha introducido
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3 / | | / |x|\ | |1 - ---|*sin(a*t) dt | \ 3 / | / 0
$$\int\limits_{0}^{3} \left(- \frac{\left|{x}\right|}{3} + 1\right) \sin{\left(a t \right)}\, dt$$
Integral((1 - |x|/3)*sin(a*t), (t, 0, 3))
Respuesta (Indefinida)
[src]
/ | // 0 for a = 0\ | / |x|\ / |x|\ || | | |1 - ---|*sin(a*t) dt = C + |1 - ---|*|<-cos(a*t) | | \ 3 / \ 3 / ||---------- otherwise| | \\ a / /
$$\int \left(- \frac{\left|{x}\right|}{3} + 1\right) \sin{\left(a t \right)}\, dt = C + \left(- \frac{\left|{x}\right|}{3} + 1\right) \left(\begin{cases} 0 & \text{for}\: a = 0 \\- \frac{\cos{\left(a t \right)}}{a} & \text{otherwise} \end{cases}\right)$$
Respuesta
[src]
/ |x| / |x|\ |1 - --- |1 - ---|*cos(3*a) | 3 \ 3 / <------- - ------------------ for And(a > -oo, a < oo, a != 0) | a a | \ 0 otherwise
$$\begin{cases} - \frac{\left(1 - \frac{\left|{x}\right|}{3}\right) \cos{\left(3 a \right)}}{a} + \frac{1 - \frac{\left|{x}\right|}{3}}{a} & \text{for}\: a > -\infty \wedge a < \infty \wedge a \neq 0 \\0 & \text{otherwise} \end{cases}$$
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/ |x| / |x|\ |1 - --- |1 - ---|*cos(3*a) | 3 \ 3 / <------- - ------------------ for And(a > -oo, a < oo, a != 0) | a a | \ 0 otherwise
$$\begin{cases} - \frac{\left(1 - \frac{\left|{x}\right|}{3}\right) \cos{\left(3 a \right)}}{a} + \frac{1 - \frac{\left|{x}\right|}{3}}{a} & \text{for}\: a > -\infty \wedge a < \infty \wedge a \neq 0 \\0 & \text{otherwise} \end{cases}$$
Piecewise(((1 - |x|/3)/a - (1 - |x|/3)*cos(3*a)/a, (a > -oo)∧(a < oo)∧(Ne(a, 0))), (0, True))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.