[微积分] 利用极坐标计算二重积分

https://wenku.baidu.com/view/3e62df30b90d6c85ec3ac670.htmlhtml

https://baijiahao.baidu.com/s?id=1614655524397070040&wfr=spider&for=pcide

1. 极坐标的定义

已知平面上一点P,在直角坐标系下坐标为(x,y),极坐标系下的坐标为spa

 

2. 推导

即将$dxdy$ 转换为:$rdrd\theta$htm

3. 计算

1) $\alpha <= \theta <= \beta$; $\varphi_1(\theta) <= \theta <= \varphi_2(\theta)$blog

2) $\alpha <= \theta <= \beta$; $0 <= r <= \varphi(\theta)$get

3) $0 <= \theta <= 2\pi$; $0 <= r <= \varphi(\theta)$io