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