Sr Examen
Integral de ye^(xy/2) dy
Solución
Ha introducido
[src]
log(3)
/
|
| x*y
| ---
| 2
| y*E dy
|
/
log(2)
$$\int\limits_{\log{\left(2 \right)}}^{\log{\left(3 \right)}} e^{\frac{x y}{2}} y\, dy$$
Integral(y*E^((x*y)/2), (y, log(2), log(3)))
Respuesta (Indefinida)
[src]
// x*y \
/ || --- |
| || 2 |
| x*y ||(-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*log(3) x*log(2) | -------- -------- | 2 2 |(-4 + 2*x*log(3))*e (-4 + 2*x*log(2))*e |--------------------------- - --------------------------- for And(x > -oo, x < oo, x != 0) | 2 2 < x x | | 2 2 | log (3) log (2) | ------- - ------- otherwise | 2 2 \
$$\begin{cases} - \frac{\left(2 x \log{\left(2 \right)} - 4\right) e^{\frac{x \log{\left(2 \right)}}{2}}}{x^{2}} + \frac{\left(2 x \log{\left(3 \right)} - 4\right) e^{\frac{x \log{\left(3 \right)}}{2}}}{x^{2}} & \text{for}\: x > -\infty \wedge x < \infty \wedge x \neq 0 \\- \frac{\log{\left(2 \right)}^{2}}{2} + \frac{\log{\left(3 \right)}^{2}}{2} & \text{otherwise} \end{cases}$$
=
=
/ x*log(3) x*log(2) | -------- -------- | 2 2 |(-4 + 2*x*log(3))*e (-4 + 2*x*log(2))*e |--------------------------- - --------------------------- for And(x > -oo, x < oo, x != 0) | 2 2 < x x | | 2 2 | log (3) log (2) | ------- - ------- otherwise | 2 2 \
$$\begin{cases} - \frac{\left(2 x \log{\left(2 \right)} - 4\right) e^{\frac{x \log{\left(2 \right)}}{2}}}{x^{2}} + \frac{\left(2 x \log{\left(3 \right)} - 4\right) e^{\frac{x \log{\left(3 \right)}}{2}}}{x^{2}} & \text{for}\: x > -\infty \wedge x < \infty \wedge x \neq 0 \\- \frac{\log{\left(2 \right)}^{2}}{2} + \frac{\log{\left(3 \right)}^{2}}{2} & \text{otherwise} \end{cases}$$
Piecewise(((-4 + 2*x*log(3))*exp(x*log(3)/2)/x^2 - (-4 + 2*x*log(2))*exp(x*log(2)/2)/x^2, (x > -oo)∧(x < oo)∧(Ne(x, 0))), (log(3)^2/2 - log(2)^2/2, True))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.