Задача 61484 1. _[ I (х? +у)ахау, О: у=х?, х=у?. ...
Условие
математика
161
Решение
★
D:
0 ≤ x ≤ 1;
x^2 ≤ y ≤ sqrt((x))
∫∫_(D)(x^2+y)dxdy= ∫_(0)^(1)[blue](∫_(sqrt(x))^(x^2) (x^2+y)dy)[/blue]dx=
= ∫_(0)^(1)[blue](x^2y+(y^2/2))|_(sqrt(x))^(x^2) [/blue]dx=
=∫_(0)^(1)[blue](x^2\sqrt(x)+(sqrt(x))^2/2)- x^2*x^2-((x^2)^2/2))[/blue]dx=
=∫_(0)^(1)[blue](x^2\sqrt(x)+(x/2)- x^4*-(x^4/2))[/blue]dx=
=(x^(7/2)/(7/2)+(1/2)(x^2/2)-(3/2)*(x^5/5))|_(0)^(1)=(2/7)+(1/4)-(3/10)=....