Задача 37224 ...

vk168562092

2019-05-18 18:16:53

Решить двойной интеграл

∫(от 0 до 1) dx ∫(от x^2 до √x) xy dy

sova

2019-05-19 09:05:47

= ∫ ^(1)_(0)(xy^2/2)|^(y=sqrt(x))_(y=x^2)dx=

= ∫ ^(1)_(0)((x*(sqrt(x))^2/2)- x*(x^2)^2/2) dx=

= ∫ ^(1)_(0)((x^2/2) - (x^5/2))dx=

=((x^3/6)-(x^6/12))|^(1)_(0)=(1/6)-(1/12)= [b]1/12[/b]