Sr Examen
Integral de sin²ax dx
Solución
Ha introducido
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1 / | | 2 | sin (a*x) dx | / 0
$$\int\limits_{0}^{1} \sin^{2}{\left(a x \right)}\, dx$$
Integral(sin(a*x)^2, (x, 0, 1))
Respuesta (Indefinida)
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/ x for a = 0
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$$\int \sin^{2}{\left(a x \right)}\, dx = C + \frac{x}{2} - \frac{\begin{cases} x & \text{for}\: a = 0 \\\frac{\sin{\left(2 a x \right)}}{2 a} & \text{otherwise} \end{cases}}{2}$$
Respuesta
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/a cos(a)*sin(a) |- - ------------- |2 2 <----------------- for And(a > -oo, a < oo, a != 0) | a | \ 0 otherwise
$$\begin{cases} \frac{\frac{a}{2} - \frac{\sin{\left(a \right)} \cos{\left(a \right)}}{2}}{a} & \text{for}\: a > -\infty \wedge a < \infty \wedge a \neq 0 \\0 & \text{otherwise} \end{cases}$$
=
=
/a cos(a)*sin(a) |- - ------------- |2 2 <----------------- for And(a > -oo, a < oo, a != 0) | a | \ 0 otherwise
$$\begin{cases} \frac{\frac{a}{2} - \frac{\sin{\left(a \right)} \cos{\left(a \right)}}{2}}{a} & \text{for}\: a > -\infty \wedge a < \infty \wedge a \neq 0 \\0 & \text{otherwise} \end{cases}$$
Piecewise(((a/2 - cos(a)*sin(a)/2)/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.