Question

高数微积分题求帮忙

第一道题算到结尾不知道怎么的结果，第二道题简单的没掌握

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Answer 1

Answer 2

(x-5)^2+(y-5)^2 =16

y= 5±√[16-(x-5)^2]
y=0, =>x=5 or 1
let
x-5=4sinu
dx=4cosu du
x=1, u=-π/2
x=4, u=π/2
Vx
=π∫(1->5) { [5+√[16-(x-5)^2] ]^2 - [5-√[16-(x-5)^2] ]^2 } dx
=20π∫(1->5) √[16-(x-5)^2] dx

=20π∫(-π/2->π/2) 16 (cosu)^2 du
=320π∫(-π/2->π/2) (cosu)^2 du
=640π∫(0->π/2) (cosu)^2 du
=320π∫(0->π/2) (1+cos2u) du
=320π[u+(1/2)sin2u]|(0->π/2)
=160π^2
ans : C

Answer 3