Question

圆域求二重积分xy

计算二重积分∫∫xydσ,其中区域D是有圆x²+y²=1 及坐标轴所围成的在第一象限的封闭区域

Answer 1

0≤x≤√(1-y²),0≤y≤1,
∫∫xydσ
=∫[0,1]dy∫[0,√(1-y²)]xydx
=(1/2)∫[0,1]dy[(1-y²)y-0]
=(1/2)∫[0,1]ydy - (1/2)∫[0,1]y^3dy
=(1/4) - (1/8)
=1/8
微积分码字很辛苦啊,原函数标注上下限那步我就省略了吧,反正都是简单的.