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