Задача 67390 ...

638f738fddba6d42a21cccd6

06.12.2022 19:54:43

∫∫(x+y)dxdy D: y=x^2-1, y=-x^2+1

5f3ea7e3faf909182968ddd9

06.12.2022 20:41:31

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∫ _(-1)^(1)( [blue]∫ _(x^2-1)^(-x^2+1)(x+y)dy[/blue])dx=

=∫ _(-1)^(1)(xy+(y^2/2))| _(x^2-1)^(-x^2+1) dx=

=∫ _(-1)^(1) [b]([/b]x(-x^2+1)+((-x^2+1)^2/2)-x*(x^2-1)-((x^2-1)^2/2)[b])[/b]dx=


=∫ _(-1)^(1) [b]([/b]-x^3+x+(1/2)x^4-x^2+(1/2)-x^3+x-(1/2)x^4+x^2-(1/2)[b])[/b]dx=

=∫ _(-1)^(1) (2x-2x^3)dx=(x^2-(2x^4/4))| _(-1)^(1)=0