Sr Examen
Integral de sin(a-bx) dx
Solución
Ha introducido
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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)
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/ //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
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/cos(a - b) cos(a) |---------- - ------ for And(b > -oo, b < oo, b != 0) < b b | \ sin(a) otherwise
$$\begin{cases} - \frac{\cos{\left(a \right)}}{b} + \frac{\cos{\left(a - b \right)}}{b} & \text{for}\: b > -\infty \wedge b < \infty \wedge b \neq 0 \\\sin{\left(a \right)} & \text{otherwise} \end{cases}$$
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/cos(a - b) cos(a) |---------- - ------ 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)/b - cos(a)/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.