轮换对称性:
\(若将D中的x与y对调,可推出D不变,则:\iint_{D} f(x,y)dxdy=\iint_{D} f(y,x)dxdy,此即为轮换对称性\)
\(\iint_{D} f(x,y)d\sigma = \iint_{D} f(x,y)dxdy\)
\(X型区域(上下型)\int_a^bdx\int_{y_1(x)}^{y_2(x)} f(x,y)dy\)
后积先定限,限内画条线,先交下曲线,后交上曲线
\(Y型区域(左右型)\int_c^ddy\int_{x_1(y)}^{x_2(y)} f(x,y)dx\)
\(d\sigma=d\theta\cdot rdr \Rightarrow \iint_Df(x,y)d\sigma =\int_\alpha^\beta d\theta\int_{r_1(\theta)}^{r_2(\theta)} f(rcos{\theta},rsin{\theta})rdr\)
\(f(x,y)在有界闭区域D上连续,\sigma_{0}是D的面积,则在D内至少存在一点(\xi,\mu),使得\iint_{D} f(x,y)d\sigma = f(\xi,\mu)\sigma_{0}\)
手机扫一扫
移动阅读更方便
你可能感兴趣的文章