演習問題

次の重積分の値を求めよ．

${\displaystyle \underset{D}{\iint }\left(x-2xy+3y\right)dxdy}$　　${\displaystyle \left(D:-1\leqq x\leqq 1,-2\leqq y\leqq 0\right)}$

次の重積分の値を求めよ．

${\displaystyle \underset{D}{\iint }\left(x^2+y^2\right)dxdy}$　　${\displaystyle \left(D:-2\leqq x\leqq 2,-2\leqq y\leqq 2\right)}$

次の重積分の値を求めよ．

${\displaystyle \underset{D}{\iint }rsin\theta drd\theta }$　　${\displaystyle \left(D:\frac{\pi }{3}\leqq \theta \leqq \pi ,0\leqq r\leqq 4\right)}$

次の重積分の値を求めよ．

${\displaystyle \underset{D}{\iint }xdxdy}$　　${\displaystyle \left(D:\frac{x}{2}+\frac{y}{4}\leqq 1,x\geqq 0,y\geqq 0\right)}$

次の重積分の値を求めよ．

${\displaystyle \underset{D}{\iint }\left(4-x-y\right)dxdy}$　　${\displaystyle \left(D:0\leqq x\leqq 2,-x\leqq y\leqq x\right)}$

次の重積分の値を求めよ．

${\displaystyle \underset{D}{\iint }{\left(x-y\right)}^{2}dxdy}$　　${\displaystyle \left(D:\left|x+2\right|\leqq 1,\left|x-2y\right|\leqq 1\right)}$