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