Sr Examen
Integral de -(e^arccos*(a*x))*a/sqrt(1-(a^2)*(x^2)) dx
Solución
Ha introducido
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1 / | | acos(a*x) | -E *a | -------------- dx | ___________ | / 2 2 | \/ 1 - a *x | / 0
$$\int\limits_{0}^{1} \frac{- e^{\operatorname{acos}{\left(a x \right)}} a}{\sqrt{- a^{2} x^{2} + 1}}\, dx$$
Integral(((-E^acos(a*x))*a)/sqrt(1 - a^2*x^2), (x, 0, 1))
Respuesta (Indefinida)
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/ | | acos(a*x) // acos(a*x) \ | -E *a ||e for a != 0| | -------------- dx = C + |< | | ___________ || 0 otherwise | | / 2 2 \\ / | \/ 1 - a *x | /
$$\int \frac{- e^{\operatorname{acos}{\left(a x \right)}} a}{\sqrt{- a^{2} x^{2} + 1}}\, dx = C + \begin{cases} e^{\operatorname{acos}{\left(a x \right)}} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}$$
Respuesta
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/ pi | -- | 2 acos(a) |- e + e for And(a > -oo, a < oo, a != 0) < | pi | -- | 2 \ -a*e otherwise
$$\begin{cases} e^{\operatorname{acos}{\left(a \right)}} - e^{\frac{\pi}{2}} & \text{for}\: a > -\infty \wedge a < \infty \wedge a \neq 0 \\- a e^{\frac{\pi}{2}} & \text{otherwise} \end{cases}$$
=
=
/ pi | -- | 2 acos(a) |- e + e for And(a > -oo, a < oo, a != 0) < | pi | -- | 2 \ -a*e otherwise
$$\begin{cases} e^{\operatorname{acos}{\left(a \right)}} - e^{\frac{\pi}{2}} & \text{for}\: a > -\infty \wedge a < \infty \wedge a \neq 0 \\- a e^{\frac{\pi}{2}} & \text{otherwise} \end{cases}$$
Piecewise((-exp(pi/2) + exp(acos(a)), (a > -oo)∧(a < oo)∧(Ne(a, 0))), (-a*exp(pi/2), True))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.