Integrale über messbare Mengen

Flächeninhalt eines Kreises

(∫_(-1)^1)(∫_(-(Sqrt[1 - (x^2)]))^((Sqrt[1 - (x^2)])))1 \[DifferentialD]y \[DifferentialD]x

int = (∫_(-r)^r)(∫_(-(Sqrt[(r^2) - (x^2)]))^((Sqrt[(r^2) - (x^2)])))1 \[DifferentialD]y \[DifferentialD]x

FullSimplify[int, r > 0]

Volumen einer Kugel in kartesischen Koordinaten

(∫_(-1)^1)(∫_(-(Sqrt[1 - (x^2)]))^((Sqrt[1 - (x^2)])))(∫_(-(Sqrt[1 - (x^2) - (y^2)]))^((Sqrt[1 - (x^2) - (y^2)])))1 \[DifferentialD]z \[DifferentialD]y \[DifferentialD]x

innere Integrale

(∫_(-(Sqrt[1 - (x^2) - (y^2)]))^((Sqrt[1 - (x^2) - (y^2)])))1 \[DifferentialD]z

(∫_(-(Sqrt[1 - (x^2)]))^((Sqrt[1 - (x^2)])))(∫_(-(Sqrt[1 - (x^2) - (y^2)]))^((Sqrt[1 - (x^2) - (y^2)])))1 \[DifferentialD]z \[DifferentialD]y // Simplify

Integral über Ellipse

(∫_0^a)(∫_0^(b (Sqrt[ 1 - ((x^2)/(a^2))])))(x^2) (y^3) \[DifferentialD]y \[DifferentialD]x