Решить двойной интеграл ∫ ∫ xydxdy
D: 0 ≤ x ≤ ≤ 2 0 ≤ y ≤ x^3 ∫∫_(D)xydxdy= ∫_(0)^(2) ([blue]∫_(0) ^(x^3)xydy[/blue])dx=∫_(0)^(2)([blue](xy^2/2)|_(0) ^(x^3)[/blue])dx=∫_(0)^(2)(x*(x^3))^2/2)dx=(1/2)∫_(0)^(2)x^(7)dx=(1/2)*(x^8/8)|_(0)^(2)=(1/2)*(2^8)/8=16