Sr Examen
Integral de (sqrt(2+x^2)-sqrt(2-x^2))/sqrt(4-x^4) dx
Solución
Ha introducido
[src]
1 / | | ________ ________ | / 2 / 2 | \/ 2 + x - \/ 2 - x | ------------------------- dx | ________ | / 4 | \/ 4 - x | / 0
$$\int\limits_{0}^{1} \frac{- \sqrt{2 - x^{2}} + \sqrt{x^{2} + 2}}{\sqrt{4 - x^{4}}}\, dx$$
Integral((sqrt(2 + x^2) - sqrt(2 - x^2))/sqrt(4 - x^4), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ / / | | | | ________ ________ | ________ | ________ | / 2 / 2 | / 2 | / 2 | \/ 2 + x - \/ 2 - x | \/ 2 - x | \/ 2 + x | ------------------------- dx = C - | ------------------------ dx + | ------------------------ dx | ________ | _____________________ | _____________________ | / 4 | / / 2\ / 2\ | / / 2\ / 2\ | \/ 4 - x | \/ -\-2 + x /*\2 + x / | \/ -\-2 + x /*\2 + x / | | | / / /
$$\int \frac{- \sqrt{2 - x^{2}} + \sqrt{x^{2} + 2}}{\sqrt{4 - x^{4}}}\, dx = C - \int \frac{\sqrt{2 - x^{2}}}{\sqrt{- \left(x^{2} - 2\right) \left(x^{2} + 2\right)}}\, dx + \int \frac{\sqrt{x^{2} + 2}}{\sqrt{- \left(x^{2} - 2\right) \left(x^{2} + 2\right)}}\, dx$$
Respuesta
[src]
1 1
/ /
| |
| 1 | -1
- | ----------- dx - | ----------- dx
| ________ | ________
| / 2 | / 2
| \/ 2 + x | \/ 2 - x
| |
/ /
0 0
$$- \int\limits_{0}^{1} \frac{1}{\sqrt{x^{2} + 2}}\, dx - \int\limits_{0}^{1} \left(- \frac{1}{\sqrt{2 - x^{2}}}\right)\, dx$$
=
=
1 1
/ /
| |
| 1 | -1
- | ----------- dx - | ----------- dx
| ________ | ________
| / 2 | / 2
| \/ 2 + x | \/ 2 - x
| |
/ /
0 0
$$- \int\limits_{0}^{1} \frac{1}{\sqrt{x^{2} + 2}}\, dx - \int\limits_{0}^{1} \left(- \frac{1}{\sqrt{2 - x^{2}}}\right)\, dx$$
-Integral(1/sqrt(2 + x^2), (x, 0, 1)) - Integral(-1/sqrt(2 - x^2), (x, 0, 1))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.