Sr Examen
Integral de x^2*dx/sqrt(64-x^6) dx
Solución
Ha introducido
[src]
2 / | | 2 | x | ------------ dx | _________ | / 6 | \/ 64 - x | / 0
$$\int\limits_{0}^{2} \frac{x^{2}}{\sqrt{64 - x^{6}}}\, dx$$
Integral(x^2/sqrt(64 - x^6), (x, 0, 2))
Respuesta (Indefinida)
[src]
// / 3\ \
|| |x | |
/ ||-I*acosh|--| | 6| |
| || \8 / |x | |
| 2 ||------------- for ---- > 1|
| x || 3 64 |
| ------------ dx = C + |< |
| _________ || / 3\ |
| / 6 || |x | |
| \/ 64 - x || asin|--| |
| || \8 / |
/ || -------- otherwise |
\\ 3 /
$$\int \frac{x^{2}}{\sqrt{64 - x^{6}}}\, dx = C + \begin{cases} - \frac{i \operatorname{acosh}{\left(\frac{x^{3}}{8} \right)}}{3} & \text{for}\: \frac{\left|{x^{6}}\right|}{64} > 1 \\\frac{\operatorname{asin}{\left(\frac{x^{3}}{8} \right)}}{3} & \text{otherwise} \end{cases}$$
Gráfica
Respuesta
[src]
2 / | | / 2 6 | | -I*x x | |---------------- for -- > 1 | | _________ 64 | | / 6 | | / x | |8* / -1 + -- | | \/ 64 | < dx | | 2 | | x | |--------------- otherwise | | ________ | | / 6 | | / x | |8* / 1 - -- | \ \/ 64 | / 0
$$\int\limits_{0}^{2} \begin{cases} - \frac{i x^{2}}{8 \sqrt{\frac{x^{6}}{64} - 1}} & \text{for}\: \frac{x^{6}}{64} > 1 \\\frac{x^{2}}{8 \sqrt{1 - \frac{x^{6}}{64}}} & \text{otherwise} \end{cases}\, dx$$
=
=
2 / | | / 2 6 | | -I*x x | |---------------- for -- > 1 | | _________ 64 | | / 6 | | / x | |8* / -1 + -- | | \/ 64 | < dx | | 2 | | x | |--------------- otherwise | | ________ | | / 6 | | / x | |8* / 1 - -- | \ \/ 64 | / 0
$$\int\limits_{0}^{2} \begin{cases} - \frac{i x^{2}}{8 \sqrt{\frac{x^{6}}{64} - 1}} & \text{for}\: \frac{x^{6}}{64} > 1 \\\frac{x^{2}}{8 \sqrt{1 - \frac{x^{6}}{64}}} & \text{otherwise} \end{cases}\, dx$$
Integral(Piecewise((-i*x^2/(8*sqrt(-1 + x^6/64)), x^6/64 > 1), (x^2/(8*sqrt(1 - x^6/64)), True)), (x, 0, 2))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.