Sr Examen
Integral de x/sqrt(16-x^4) dx
Solución
Ha introducido
[src]
2 / | | x | ------------ dx | _________ | / 4 | \/ 16 - x | / 0
$$\int\limits_{0}^{2} \frac{x}{\sqrt{16 - x^{4}}}\, dx$$
Integral(x/sqrt(16 - x^4), (x, 0, 2))
Respuesta (Indefinida)
[src]
// / 2\ \
|| |x | |
||-I*acosh|--| | 4| |
/ || \4 / |x | |
| ||------------- for ---- > 1|
| x || 2 16 |
| ------------ dx = C + |< |
| _________ || / 2\ |
| / 4 || |x | |
| \/ 16 - x || asin|--| |
| || \4 / |
/ || -------- otherwise |
\\ 2 /
$$\int \frac{x}{\sqrt{16 - x^{4}}}\, dx = C + \begin{cases} - \frac{i \operatorname{acosh}{\left(\frac{x^{2}}{4} \right)}}{2} & \text{for}\: \frac{\left|{x^{4}}\right|}{16} > 1 \\\frac{\operatorname{asin}{\left(\frac{x^{2}}{4} \right)}}{2} & \text{otherwise} \end{cases}$$
Gráfica
Respuesta
[src]
2 / | | / 4 | | -I*x x | |---------------- for -- > 1 | | _________ 16 | | / 4 | | / x | |4* / -1 + -- | | \/ 16 | < dx | | x | |--------------- otherwise | | ________ | | / 4 | | / x | |4* / 1 - -- | | \/ 16 | \ | / 0
$$\int\limits_{0}^{2} \begin{cases} - \frac{i x}{4 \sqrt{\frac{x^{4}}{16} - 1}} & \text{for}\: \frac{x^{4}}{16} > 1 \\\frac{x}{4 \sqrt{1 - \frac{x^{4}}{16}}} & \text{otherwise} \end{cases}\, dx$$
=
=
2 / | | / 4 | | -I*x x | |---------------- for -- > 1 | | _________ 16 | | / 4 | | / x | |4* / -1 + -- | | \/ 16 | < dx | | x | |--------------- otherwise | | ________ | | / 4 | | / x | |4* / 1 - -- | | \/ 16 | \ | / 0
$$\int\limits_{0}^{2} \begin{cases} - \frac{i x}{4 \sqrt{\frac{x^{4}}{16} - 1}} & \text{for}\: \frac{x^{4}}{16} > 1 \\\frac{x}{4 \sqrt{1 - \frac{x^{4}}{16}}} & \text{otherwise} \end{cases}\, dx$$
Integral(Piecewise((-i*x/(4*sqrt(-1 + x^4/16)), x^4/16 > 1), (x/(4*sqrt(1 - x^4/16)), True)), (x, 0, 2))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.