1 / | | 2 | x | ------------ dx | _________ | / 2 2 | \/ a - x | / 0
Integral(x^2/sqrt(a^2 - x^2), (x, 0, 1))
// _________ \ || / 2 | || / x | || 2 /x\ I*a*x* / -1 + -- | || I*a *acosh|-| / 2 | 2| | || \a/ \/ a |x | | / || - ------------- - --------------------- for |--| > 1| | || 2 2 | 2| | | 2 || |a | | | x || | | ------------ dx = C + |< 2 /x\ | | _________ ||a *asin|-| 3 | | / 2 2 || \a/ x a*x | | \/ a - x ||---------- + ------------------ - ---------------- otherwise | | || 2 ________ ________ | / || / 2 / 2 | || / x / x | || 2*a* / 1 - -- 2* / 1 - -- | || / 2 / 2 | || \/ a \/ a | \\ /
1 / | | / _________ | | / 2 | | / x | | I*a* / -1 + -- | | / 2 2 2 | | \/ a I*a I*x x | |- ------------------- - ----------------- - ------------------- for ---- > 1 | | 2 _________ _________ | 2| | | / 2 / 2 |a | | | / x / x | | 2* / -1 + -- 2*a* / -1 + -- | < / 2 / 2 dx | | \/ a \/ a | | | | 4 2 2 | | x x 3*x | | ---------------- - --------------- + ------------------ otherwise | | 3/2 3/2 ________ | | / 2\ / 2\ / 2 | | 3 | x | | x | / x | | 2*a *|1 - --| 2*a*|1 - --| 2*a* / 1 - -- | | | 2| | 2| / 2 | \ \ a / \ a / \/ a | / 0
=
1 / | | / _________ | | / 2 | | / x | | I*a* / -1 + -- | | / 2 2 2 | | \/ a I*a I*x x | |- ------------------- - ----------------- - ------------------- for ---- > 1 | | 2 _________ _________ | 2| | | / 2 / 2 |a | | | / x / x | | 2* / -1 + -- 2*a* / -1 + -- | < / 2 / 2 dx | | \/ a \/ a | | | | 4 2 2 | | x x 3*x | | ---------------- - --------------- + ------------------ otherwise | | 3/2 3/2 ________ | | / 2\ / 2\ / 2 | | 3 | x | | x | / x | | 2*a *|1 - --| 2*a*|1 - --| 2*a* / 1 - -- | | | 2| | 2| / 2 | \ \ a / \ a / \/ a | / 0
Integral(Piecewise((-i*a*sqrt(-1 + x^2/a^2)/2 - i*a/(2*sqrt(-1 + x^2/a^2)) - i*x^2/(2*a*sqrt(-1 + x^2/a^2)), x^2/|a^2| > 1), (x^4/(2*a^3*(1 - x^2/a^2)^(3/2)) - x^2/(2*a*(1 - x^2/a^2)^(3/2)) + 3*x^2/(2*a*sqrt(1 - x^2/a^2)), True)), (x, 0, 1))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.