二重积分∫∫(D的区域是x²+y²≤9)√(9-x²-y²)dσ=?
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![二重积分∫∫(D的区域是x²+y²≤9)√(9-x²-y²)dσ=?](/uploads/image/z/10893339-27-9.jpg?t=%E4%BA%8C%E9%87%8D%E7%A7%AF%E5%88%86%E2%88%AB%E2%88%AB%EF%BC%88D%E7%9A%84%E5%8C%BA%E5%9F%9F%E6%98%AFx%26%23178%3B%2By%26%23178%3B%E2%89%A49%EF%BC%89%E2%88%9A%EF%BC%889-x%26%23178%3B-y%26%23178%3B%EF%BC%89d%CF%83%3D%3F)
二重积分∫∫(D的区域是x²+y²≤9)√(9-x²-y²)dσ=?
二重积分∫∫(D的区域是x²+y²≤9)√(9-x²-y²)dσ=?
二重积分∫∫(D的区域是x²+y²≤9)√(9-x²-y²)dσ=?
这个用极坐标代换啦
x=pcosa,y=psina,a∈[0,2π],p∈[0,9]
∫∫(D的区域是x²+y²≤9)√(9-x²-y²)dσ
=∫[0,9]∫[0,2π]√(9-p^2)pdpda
=∫[0,9]√(9-p^2)pdp∫[0,2π]da
=-1/2*2/3(9-p^2)^(3/2)[0,9]*a[0,2π]
=18π