Гость » Пн окт 08, 2018 10:37 pm
[tex]\int_L\bar{z}Rezdz=\int_{L}(x-iy)xd(x+i.x^2)=\int_0^{-1}(x-i.x^2).xd(x+i.x^2)=[/tex]
[tex]=\int_0^{-1}x^2d(x+i.x^2)-i.\int_0^{-1}x^3d(x+i.x^2)=\int_0^{-1}x^2(1+2i.x)dx-i\int_0^{-1}x^3(1+2ix)dx=[/tex]
[tex]=\int_0^{-1}x^2dx+2i\int_0^{-1}x^3dx-i\int_0^{-1}x^3dx-2.i^2.\int_0^{-1}x^4dx=[/tex]
[tex]=\frac{x^3}{3}|_0^{-1}+2\cdot\frac{x^5}{5}|_0^{-1}+i\cdot\frac{x^4}{4}|_0^{-1}=[/tex]
[tex]=-\frac{1}{3}-\frac{2}{5}+i\cdot\frac{1}{4}=\frac{-11}{60}+\frac{1}{4}\cdot i[/tex]