Задача 70999 ...

6446c9796e916e3d0082e45c

24.04.2023 21:37:14

Вычислить двойной интеграл (18*x^2*y^2+8xy)dxdy. D:x=1. y=-x^2. y=∛x

5f3ea7e3faf909182968ddd9

24.04.2023 23:20:44

★

0 ≤ х ≤ 1
-x^2 ≤ y ≤ ∛x

= ∫^(1) _(0)dx ∫^(∛x) _(-x^2)(8xy+18x^2y^2)dy=∫^(1) _(0)(8x*(y^2/2)+18x^2*(y^3/3))|^(∛x) _(-x^2)dx =

=∫^(1) _(0)(4x*(∛x)^2+6x^2*(∛x)^3-4x*(-x^2)^2-6x^2*(-x^2)^3)dx=

=∫^(1) _(0)(4x^(5/3)+6x^3-4x^5+6x^8)dx=(4*(x^(8/3)/(8/3)+6*(x^4/4)-4*(x^6/6)+6*(x^9/9))|^(1)_(0)=

=+(3/2)+(3/2)-(2/3)+(2/3)=[b]3[/b]