Question

Помогите срочноооооо

Answer 1

$1)\ \ \int\limits^{-1}_{-2}\, dx\int\limits^0_{-(2+x)}f(x,y)\, dy+\int\limits^0_{-1}\, dx\int\limits^0_{\sqrt[3]{x}}\, f(x,y)\, dy=\int\limits^0_{-1}\, dy\int \limits _{-(2+y)}^{y^3}\, f(x,y)\, dx$

$2)\ \ D:\ \left \{ {{3\leq x\leq 4} \atop {1\leq y\leq 2}} \right.\ \ \ \ \iint \limits _{D}\dfrac{dx\, dy}{(x+y)^2}=\int\limits^4_3\, dx\int\limits^2_1\, \dfrac{dy}{(x+y)^2}=\int\limits^4_3\, dx\, \dfrac{(x+y)^{-1}}{-1}\Big|_1^2=\\\\\\=\int\limits^4_3\, \Big(\dfrac{1}{x+2}-\dfrac{1}{x+1}\Big)\, dx=\Big(ln|x+2|-ln|x+1|\Big)\Big|_3^4=\\\\\\=ln6-ln5-(ln5-ln4)=ln\dfrac{24}{25}$