# dϕ̌vZ

1. ̏dϕvZD
 ${\int }_{0}^{2}{\int }_{\frac{y}{2}}^{1}\left(x+y\right)dxdy$
 ${\int }_{0}^{1}{\int }_{0}^{1-x}\left({x}^{2}-2y\right)dydx$
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 ${\int }_{0}^{\pi }{\int }_{0}^{\pi }sin\left(x+y\right)dxdy$
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2. ̏dϕvZD @
 ${\iint }_{D}ydxdy\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\left(D:0\le x\le 1,0\le y\le {x}^{2}\right)$ ${\iint }_{D}\left({x}^{3}+xy\right)dxdy\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\left(D:0\le y\le 1,0\le x\le \sqrt{y}\right)$ ${\iint }_{D}\left({x}^{2}-2y\right)dxdy\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\left(D:x+y\le 1,x\ge 0,y\ge 0\right)$ @ $\int \int \mathrm{log}xydxdy$           $\left(D:1\le x\le 2,1\le y\le 2\right)$ ${\iint }_{D}\left(2x-y\right)dxdy\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\left(\text{\hspace{0.17em}}D\text{\hspace{0.17em}}:\text{\hspace{0.17em}}\text{\hspace{0.17em}}-3\leqq x\leqq 3\text{\hspace{0.17em}},\text{\hspace{0.17em}}0\leqq y\leqq 3\text{\hspace{0.17em}}\right)$ ${\iint }_{D}x{y}^{2}dxdy\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\left(\text{\hspace{0.17em}}D\text{\hspace{0.17em}}:\text{\hspace{0.17em}}0\leqq x\leqq 2\text{\hspace{0.17em}},\text{\hspace{0.17em}}-2\leqq y\leqq 1\text{\hspace{0.17em}}\right)$ ${\iint }_{D}\left(x-2xy+3y\right)dxdy\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\left(\text{\hspace{0.17em}}D\text{\hspace{0.17em}}:\text{\hspace{0.17em}}-1\leqq x\leqq 1\text{\hspace{0.17em}},\text{\hspace{0.17em}}-2\leqq y\leqq 0\text{\hspace{0.17em}}\right)$ ${\iint }_{D}\left({x}^{2}+{y}^{2}\right)dxdy\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\left(\text{\hspace{0.17em}}D\text{\hspace{0.17em}}:\text{\hspace{0.17em}}-2\leqq x\leqq 2\text{\hspace{0.17em}},\text{\hspace{0.17em}}-2\leqq y\leqq 2\text{\hspace{0.17em}}\right)$ ${\iint }_{D}sin\left(x+y\right)dxdy\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\left(\text{\hspace{0.17em}}D\text{\hspace{0.17em}}:\text{\hspace{0.17em}}0\leqq x\leqq \pi \text{\hspace{0.17em}},\text{\hspace{0.17em}}0\leqq y\leqq \pi \text{\hspace{0.17em}}\right)$ ${\iint }_{D}2xcosydxdy\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\left(\text{\hspace{0.17em}}D\text{\hspace{0.17em}}:\text{\hspace{0.17em}}0\leqq x\leqq \frac{\pi }{2}\text{\hspace{0.17em}},\text{\hspace{0.17em}}\frac{\pi }{6}\leqq y\leqq \frac{\pi }{2}\text{\hspace{0.17em}}\right)$ ${\iint }_{D}rsin\theta drd\theta \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\left(\text{\hspace{0.17em}}D\text{\hspace{0.17em}}:\text{\hspace{0.17em}}\frac{\pi }{3}\leqq \theta \leqq \pi \text{\hspace{0.17em}},\text{\hspace{0.17em}}0\leqq r\leqq 4\text{\hspace{0.17em}}\right)$ ${\iint }_{D}xdxdy\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\left(\text{\hspace{0.17em}}D\text{\hspace{0.17em}}:\text{\hspace{0.17em}}\frac{x}{2}+\frac{y}{4}\leqq 1\text{\hspace{0.17em}},\text{\hspace{0.17em}}x\geqq 0\text{\hspace{0.17em}},\text{\hspace{0.17em}}y\geqq 0\text{\hspace{0.17em}}\right)$ ${\iint }_{D}\left(x+y\right)dxdy\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\left(\text{\hspace{0.17em}}D\text{\hspace{0.17em}}:\text{\hspace{0.17em}}\frac{x}{3}+y\leqq 2\text{\hspace{0.17em}},\text{\hspace{0.17em}}x\geqq 0\text{\hspace{0.17em}},\text{\hspace{0.17em}}y\geqq 0\text{\hspace{0.17em}}\right)$ ${\iint }_{D}xydxdy\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\left(\text{\hspace{0.17em}}D\text{\hspace{0.17em}}:\text{\hspace{0.17em}}2x+\frac{y}{2}\leqq 1\text{\hspace{0.17em}},\text{\hspace{0.17em}}x\geqq 0\text{\hspace{0.17em}},\text{\hspace{0.17em}}y\geqq 0\text{\hspace{0.17em}}\right)$ ${\iint }_{D}\left({x}^{2}+{y}^{2}\right)dxdy\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\left(\text{\hspace{0.17em}}D\text{\hspace{0.17em}}:\text{\hspace{0.17em}}x+y\leqq 2\text{\hspace{0.17em}},\text{\hspace{0.17em}}x\geqq 0\text{\hspace{0.17em}},\text{\hspace{0.17em}}y\geqq 0\text{\hspace{0.17em}}\right)$ ${\iint }_{D}sin\left(x+y\right)dxdy\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\left(\text{\hspace{0.17em}}D\text{\hspace{0.17em}}:\text{\hspace{0.17em}}x+y\leqq \pi \text{\hspace{0.17em}},\text{\hspace{0.17em}}x\geqq 0\text{\hspace{0.17em}},\text{\hspace{0.17em}}y\geqq 0\text{\hspace{0.17em}}\right)$ ${\iint }_{D}\left(4-x-y\right)dxdy\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\left(\text{\hspace{0.17em}}D\text{\hspace{0.17em}}:\text{\hspace{0.17em}}0\leqq x\leqq 2\text{\hspace{0.17em}},\text{\hspace{0.17em}}-x\leqq y\leqq x\text{\hspace{0.17em}}\right)$ ${\iint }_{D}{\left(x-y\right)}^{2}dxdy\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\left(\text{\hspace{0.17em}}D\text{\hspace{0.17em}}:\text{\hspace{0.17em}}|x+2|\leqq 1\text{\hspace{0.17em}},\text{\hspace{0.17em}}|x-2y|\leqq 1\text{\hspace{0.17em}}\right)$ ${\iint }_{D}xdxdy\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\left(\text{\hspace{0.17em}}D\text{\hspace{0.17em}}:\text{\hspace{0.17em}}0\leqq y\leqq 3x-{x}^{2}\text{\hspace{0.17em}}\right)$ ${\iint }_{D}\left(x+2\right)dxdy\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\left(\text{\hspace{0.17em}}D\text{\hspace{0.17em}}:\text{\hspace{0.17em}}-1\leqq x\leqq 1\text{\hspace{0.17em}},\text{\hspace{0.17em}}0\leqq y\leqq {x}^{2}+1\text{\hspace{0.17em}}\right)$ ${\iint }_{D}\left(2xy+3{y}^{2}\right)dxdy\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\left(\text{\hspace{0.17em}}D\text{\hspace{0.17em}}:\text{\hspace{0.17em}}{x}^{2}\leqq y\leqq x\text{\hspace{0.17em}}\right)$ ${\iint }_{D}\left(2x+y\right)dxdy\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\left(\text{\hspace{0.17em}}D\text{\hspace{0.17em}}:\text{\hspace{0.17em}}{x}^{2}\leqq y\leqq x+2\text{\hspace{0.17em}}\right)$ ${\iint }_{D}xydxdy\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\left(D:{x}^{2}\leqq y\leqq x\right)$ ${\iint }_{D}{y}^{2}dxdy\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\left(D:{x}^{2}+{y}^{2}\leqq 9,x\geqq 0\right)$ ${\iint }_{D}\left({x}^{2}-{y}^{2}\right)\left(x+y\right)dxdy$ @@$\left(D:0\le x+y\le 2,-1\le x-y\le 2\right)$ ${\iint }_{D}4\left({x}^{2}+2xy+{y}^{2}\right)\left({x}^{2}-{y}^{2}\right)dxdy$ @@$\left(D:0\le x+y\le 2,-1\le x-y\le 2\right)$ ${\iint }_{D}{x}^{3}+{y}^{3}dxdy$ @@$\left(D:2\le x+y\le 5,-6\le x-2y\le 0\right)$

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