Двоен интеграл

[Гост]

[tex]\int[/tex][tex]\int[/tex] (1+8x)dxdy.
D={(x,y): 1<=x<=2 , 2<=y<=5}

[ptj]

[tex]\int\limits_{2}^{5}\int\limits_{1}^{2} (1+8x)\,dx\,dy=\int\limits_{2}^{5}\bigg(4x^2+x+C_1\begin{array}{|l} 2 \\ 1 \end{array}\bigg)\,dy=\int\limits_{2}^{5}\bigg(4.2^2+2+C_1-(4.1^2+1+C_1)\bigg)\,dy=\int\limits_{2}^{5}13\,dy=[/tex]
[tex]=13y+C_2\begin{array}{|l} 5 \\ 2 \end{array}=13.5+C_2-(13.2+C_2)=39[/tex]