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