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