二重積分奇偶性判斷,請看圖
Y=X在D1 D2關(guān)于x軸對稱,在D3 D4關(guān)于Y軸對稱,為什么在D1 D2就為奇函數(shù),在D3 D4為偶函數(shù)(特別是這點(diǎn)搞不懂)...講得詳細(xì)點(diǎn),以后碰到類似的題目怎么判斷~
![](http://e.hiphotos.baidu.com/zhidao/wh%3D600%2C800/sign=3fa5cb09ca8065387bbfac15a7ed8d7c/0bd162d9f2d3572cbd69d29b8a13632763d0c3ea.jpg)
區(qū)域關(guān)于x軸對稱,要看被積函數(shù)關(guān)于y的奇偶性;
區(qū)域關(guān)于y軸對稱,要看被積函數(shù)關(guān)于x的奇偶性.
圖中D1、D2關(guān)于x軸對稱,被積函數(shù)y是關(guān)于y的奇函數(shù),所以積分為零;
D3、D4關(guān)于y軸對稱,被積函數(shù)y是關(guān)于x的偶函數(shù),所以
![](http://b.hiphotos.baidu.com/zhidao/wh%3D600%2C800/sign=69529dafbc3eb1354492bfbd962e84eb/902397dda144ad34b0da36c0d0a20cf431ad8514.jpg)