Sr Examen
Integral de ye^(yx/2) dy
Solución
Ha introducido
[src]
1 / | | y*x | --- | 2 | y*E dy | / 0
$$\int\limits_{0}^{1} e^{\frac{x y}{2}} y\, dy$$
Integral(y*E^((y*x)/2), (y, 0, 1))
Respuesta (Indefinida)
[src]
// y*x \
/ || --- |
| || 2 |
| y*x ||(-4 + 2*x*y)*e 2 |
| --- ||----------------- for x != 0|
| 2 || 2 |
| y*E dy = C + |< x |
| || |
/ || 2 |
|| y |
|| -- otherwise |
|| 2 |
\\ /
$$\int e^{\frac{x y}{2}} y\, dy = C + \begin{cases} \frac{\left(2 x y - 4\right) e^{\frac{x y}{2}}}{x^{2}} & \text{for}\: x^{2} \neq 0 \\\frac{y^{2}}{2} & \text{otherwise} \end{cases}$$
Respuesta
[src]
/ x | - | 2 |4 (-4 + 2*x)*e <-- + ------------- for And(x > -oo, x < oo, x != 0) | 2 2 |x x | \ 1/2 otherwise
$$\begin{cases} \frac{\left(2 x - 4\right) e^{\frac{x}{2}}}{x^{2}} + \frac{4}{x^{2}} & \text{for}\: x > -\infty \wedge x < \infty \wedge x \neq 0 \\\frac{1}{2} & \text{otherwise} \end{cases}$$
=
=
/ x | - | 2 |4 (-4 + 2*x)*e <-- + ------------- for And(x > -oo, x < oo, x != 0) | 2 2 |x x | \ 1/2 otherwise
$$\begin{cases} \frac{\left(2 x - 4\right) e^{\frac{x}{2}}}{x^{2}} + \frac{4}{x^{2}} & \text{for}\: x > -\infty \wedge x < \infty \wedge x \neq 0 \\\frac{1}{2} & \text{otherwise} \end{cases}$$
Piecewise((4/x^2 + (-4 + 2*x)*exp(x/2)/x^2, (x > -oo)∧(x < oo)∧(Ne(x, 0))), (1/2, True))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.