Задача 58025 help me pls...

6028ed4d3cfdeb46290c8b33

21.02.2021 09:54:06

help me pls

5f3ea7e3faf909182968ddd9

21.02.2021 10:34:03

★

∫∫_(G) xydxdy= ∫ ^(2)_(0,5)[blue] [b](∫^(2,5-x)_(1/x) xydy)[/b][/blue]dx= ∫ ^(2)_(0,5)x*[blue] [b](∫^(2,5-x)_(1/x) ydy)[/b][/blue]dx=


=∫ ^(2)_(0,5)x*[blue] [b](y^2/2))|^(2,5-x)_(1/x))[/b][/blue]dx=

=∫ ^(2)_(0,5)x*[blue] [b]((2,5-x)^2/2)-(1/x)^2/2)[/b][/blue]dx=

=∫ ^(2)_(0,5)x*(1/2)*(6,25-5x+x^2-(1/x^2))dx=

=(1/2)∫ ^(2)_(0,5)(6,25x-5x^2+x^3-(1/x))dx=

=(1/2)*(6,25*(x^2/2)-5*(x^3/3)+(x^4/4)-ln|x|)|^(2)_(0,5)=


=(1/2)*(6,25*(2^2/2)-5*(2^3/3)+(2^4/4)-ln|2|)- (1/2)*(6,25*(0,5^2/2)-5*(0,5^3/3)+(0,5^4/4)-ln|0,5|)=

=6,25-(20/3)+2-(1/2)ln2-(1/16)*6,25+(5/48)-(1/128)+(1/2)ln(1/2)=...



ln(1/2)=-ln2